WHY PEOPLE SEE GHOSTS
|
|
|
- Silvester Griffith
- 10 years ago
- Views:
Transcription
1 The Sciece Behid WHY PEOPLE SEE GHOSTS (AND GODS, ANGELS, DEMONS, AND ALIENS AND WHY THEY FLOAT, FLY, AND TRAVEL OUT OF THEIR BODIES) By Michael Shermer ad Pat Lise 500 years ago demos hauted our world, ad icubi ad succubi tormeted their victims as they lay asleep i their beds. 200 years ago spirits of the departed made bedside visits. More recetly gree ad grey alies bega to molest people i their sleep. What is goig o here? Are these mysterious visitors i our world or i our mids? They are i our mids. All experiece is mediated by the brai, which cosists of about a hudred billio euros with a thousad trillio syaptic coectios betwee them. No woder the brai is capable of such sublime ideas as evolutio ad big bag cosmology. But it also meas that uder a variety of coditios the brai is capable of geeratig extraordiary experieces that are ot real. 1 PSYCHOACTIVE DRUGS The ability of halluciogeic drugs to trigger preteratural experieces are well documeted. A sese of floatig ad flyig may be stimulated by atropie ad other belladoa alkaloids, which are foud i madrake or jimso weed ad were used by Europea witches ad Native America shamas, probably for this very purpose. Dissociative aesthetics such as the ketamies are kow to iduce out-of-body experieces. Igestio of methyleedioxyamphetamie (MDA) may brig back log-forgotte memories ad produce the feelig of age regressio, while di-methyl-tryptamie (DMT) AKA the spirit molecule causes the dissociatio of the mid from the body ad is the halluciogeic substace i ayahuasca, a drug take by South America shama. People takig DMT report I o loger have a body, ad I am fallig, flyig, or liftig up.
2 2 MEDITATION I the 2001 book Why God Wo t Go Away, euroscietist Adrew Newberg reported that brai scas made of meditatig Buddhist moks ad prayig Fracisca us idicate strikigly low activity i the posterior superior parietal lobe, a regio of the brai the authors have dubbed the Orietatio Associatio Area (OAA). The OAA s job is to oriet the body i physical space, ad people with damage to this area have a difficult time egotiatig their way aroud a house, sometimes eve bumpig ito objects because their brai does ot process the object as somethig separate from their body. Whe the OAA is booted up ad ruig smoothly there is a sharp distictio betwee self ad o-self. Whe OAA is i sleep mode as i deep meditatio ad prayer that divisio breaks dow, leadig to a blurrig of the lies betwee reality ad fatasy, ad betwee feelig i body ad out of body. Perhaps this is what happes to moks who experiece a sese of oeess with the uiverse, or with us who feel the presece of God, or with alie abductees who float up out of their beds to joi with the mother ship. 3 BRAIN DAMAGE The reowed eurologist Oliver Sacks, best kow for his remarkable work i awakeig the catatoic brais of ecephalitis victims as portrayed i the popular 1990 film Awakeigs (starrig Robi Williams as Sacks), has writte a umber of books describig the bizarre halluciatios experieced by his patiets such as the ma who mistook his wife for a hat which are ievitably iterpreted by the experiecers as exteral to their brai. Oe elderly patiet who suffered from macular degeeratio ad had completely lost her visio was diagosed by Sacks with Charles Boett Sydrome because of her suite of complex visual halluciatios, icludig ad especially faces with distorted teeth ad eyes. Aother patiet developed a tumor i her visual cortex ad soo after bega halluciatig cartoos most memorably Kermit the Frog that were trasparet ad covered oly half of her visual field. I fact, says Sacks, about 10% of visually impaired people experiece visual halluciatios. Brai scas of halluciatig patiets show that the visual cortex is activated durig these phatasms. Durig geometric halluciatios it is the primary visual cortex that is most active the part of the brai that perceives patters (but ot images). Halluciatios that iclude images such as faces are associated with more activity i the temporal lobe s fusiform area i the temporal lobe, which is ivolved i the recogitio of faces (people with damage to this area caot recogize faces, ad stimulatio of the area causes people to spotaeously see faces). 4 COMAS I Ebe Alexader s bestsellig book Proof of Heave, the Harvard professor recouts his Near-Death Experiece (NDE) durig a meigitis-iduced coma i which he says he wet to heave. Did he? Not likely. First, Alexader claims that his cortex was completely shut dow ad that My ear-death experiece took place ot while my cortex was malfuctioig, but while it was simply off. Ad yet the oly way he could remember the experiece is if his brai was o. Ad there s a reaso they re called Near Death Experieces: the people who have them are ot actually dead. As well, as Oliver Sacks otes i his 2012 book Halluciatios, migraie headaches also produce halluciatios, which Sacks himself has experieced, icludig a shimmerig light that was dazzligly bright : It expaded, becomig a eormous arc stretchig from the groud to the sky, with sharp, glitterig, zigzaggig borders ad brilliat blue ad orage colors. Compare Sacks experiece to that of Eba Alexader s trip to heave, where he was i a place of clouds. Big, puffy, pik-white oes that showed up sharply agaist the deep blue-black sky. Higher tha the clouds immeasurably higher flocks of trasparet, shimmerig beigs arced across the sky, leavig log, streamerlike lies behid them. Dr. Sacks explais that the reaso halluciatios seem so real is that they deploy the very same systems i the brai that actual perceptios do. Whe oe halluciates voices, the auditory pathways are activated; whe oe halluciates a face, the fusiform face area, ormally used to perceive ad idetify faces i the eviromet, is stimulated. Sacks cocludes: The oe most plausible hypothesis i Dr. Alexader s case, the, is that his NDE occurred ot durig his coma, but as he was surfacig from the coma ad his cortex was returig to full fuctio. It is curious that he does ot allow this obvious ad atural explaatio, but istead isists o a superatural oe.
3 5 SENSED PRESENCE EFFECT There is a pheomeo well-kow amog moutai climbers, polar explorers, isolated sailors, ad edurace athletes called the sesed-presece effect the sese that someoe or somethig else is with us. Coditios associated with a sesed presece iclude: mootoy, darkess, barre ladscapes, isolatio, cold, ijury, dehydratio, huger, fatigue, fear, ad sleep deprivatio. Charles Lidbergh sesed ghostly preseces o his tras-atlatic flight to Paris. The famous Austria moutaieer Herma Buhl sesed a presece after summitig the 26,660 foot Naga Parbat: I see two dots. I could shout with joy. I ca hear their voices too, someoe calls Herma, but the I realize that they are rocks. I set off agai subdued. This realizatio happes frequetly. I hear voices, hear my ame really clearly [but they are oly] halluciatios. I had a extraordiary feelig that I was ot aloe. Whatever its immediate cause (temperature, altitude, hypoxia, physical exhaustio, sleep deprivatio, starvatio, loeliess, fear), a deeper cause of the sese-presece effect is to be foud i the brai: (1) A extesio of the ormal sesed presece we experiece of real people aroud us; (2) A coflict betwee the low-road of emotios ad the high-road of reaso; (3) A coflict withi the body schema, or our physical sese of self, i which the brai is tricked ito thikig that there HERRRRMANN! is aother you; (4) A coflict withi the mid schema, or our psychological sese of self, i which the mid is tricked ito thikig that there is aother mid. 6 NATURAL-BORN DUALISTS Yale Uiversity psychologist Paul Bloom says that we are atural-bor dualists. Childre ad adults alike, for example, speak of my body, as if my ad body are two differet etities. I a experimet Bloom told youg childre a story about a mouse that gets muched by a alligator. The childre agree that the mouse s body is dead it does ot eed to go to the bathroom, it ca t hear, ad its brai o loger works. However, they isist that the mouse is still hugry, cocered about the alligator, ad wats to go home. This is the foudatio for the more articulated view of the afterlife you usually fid i older childre ad adults, Bloom says. Oce childre lear that the brai is ivolved i thikig, they do t take it as showig that the brai is the source of metal life; they do t become materialists. Rather, they iterpret thikig i a arrow sese, ad coclude that the brai is a cogitive prosthesis, somethig added to the soul to ehace its computig power. The reaso dualism is ituitive is that the brai does ot perceive itself, ad so imputes metal activity to a separate source. Halluciatios of preteratural beigs such as ghosts, gods, agels, ad alies are perceived as real etities, Out-of-Body ad Near-Death Experieces are processed as exteral evets, ad the patter of iformatio that is our memories, persoality, ad self is sesed as a soul. 7 DOPAMINE Explorig the eurochemistry of superstitio ad magical thikig, psychologists Peter Brugger ad Christie Mohr foud that people with high levels of dopamie are more likely to fid sigificace i coicideces ad pick out meaig ad patters where there are oe. I oe study, they gave 40 subjects L-Dopa the drug used for Parkiso s Disease patiets that icreases the levels of dopamie i the brai ad foud that the boost of dopamie caused people to idetify scrambled faces ad real ad jumbled words as ormal. Why? Dopamie icreases the rate of eural firig i associatio with patter recogitio, which meas that syaptic coectios betwee euros are likely to icrease i respose to a perceived patter. Icreasig dopamie icreases patter detectio, ad other scietists have foud that dopamie ot oly ehaces learig but i higher doses ca also trigger symptoms of psychosis such as halluciatios.
4 8 RIGHT BRAIN v. LEFT BRAIN Carl Saga wrote: There is o doubt that right-hemisphere ituitive thikig may perceive patters ad coectios too difficult for the left hemisphere; but it may also detect patters where oe exist. Skeptical ad critical thikig is ot a hallmark of the right hemisphere. I split-brai experimets Peter Brugger preseted subjects with strigs of letters formig either a word or osese to either the left visual field or the right visual field, istructig the subjects to respod whe they recogized a word. The subjects also rated their belief i ESP o a 6-poit scale. Results: skeptics had greater left hemispheric domiace compared to believers, ad believers had superior right hemispheric performaces compared to skeptics. 9 SLEEP ANOMALIES & LUCID DREAMS Alie abductio experieces typically occur durig sleep ad strogly resemble hypagogic (just after fallig asleep) ad hypopompic (just before wakig up) halluciatios. Other dream states such as Lucid dreamig ad sleep paralysis also cotai compoets that parallel the abductio experiece. Hypagogic ad hypopompic halluciatios occur i the fuzzy borderlads betwee wakefuless ad sleep, whe our coscious brai slips ito ucosciousess as we fall asleep, or trasitios ito wakefuless from sleep. Reality ad fatasy blur. Multiple sesory modalities may be ivolved, icludig seeig ad hearig thigs that are ot actually there such as represetatioal images, geometric patters, speckles, or lies. Halluciatory images may be i black-ad-white or i color, still or movig, flat or 3-D, ad sometimes eve iclude the spiralig tuels reported by people who have Out-of-Body ad Near-Death experieces. Halluciatios ca also be auditory such as hearig your ame called, or the soud of a doorbell or kockig, ad eve fragmets of speech from others imagied to be i the room. Lucid dream images are eve more vivid because the sleepig perso is aware that he or she is asleep ad dreamig ad ca participate i ad alter the dream itself. Sleep paralysis is a type of lucid dream i which the dreamer, aware of the dream, also seses paralysis, pressure o chest, presece of a beig i the room, floatig, flyig, fallig, or leavig oe s body, with a emotioal compoet that icludes a elemet of terror, but sometimes also excitemet, exhilaratio, rapture, or ecstasy. 10 PATTERNICITY Imagie that you are a homiid o the plais of Africa three millio years ago. You hear a rustle i the grass. Is it just the wid or is it a dagerous predator? If you assume that the rustle i the grass is a dagerous predator but it turs out that it is just the wid, you have made a Type I Error i cogitio, also kow as a false positive, or believig somethig is real whe it is ot. That is, you have foud a oexistet patter. No harm. You move away from the rustlig soud, become more alert ad cautious, ad fid aother path to your destiatio. But if you assume that the rustle i the grass is just the wid but it turs out that it is a dagerous predator, you have made a Type II Error i cogitio, also kow as a false egative, or ot believig somethig is real whe it is, i this case a dagerous predator. You re luch! You are o loger a member of the homiid gee pool. Our brais are belief egies, evolved patter-recogitio machies that coect the dots ad create meaig out of the patters that we thik we see i ature. Sometimes (A) really is coected to (B), sometimes it is ot. The baseball player who does t shave (A) ad hits a home ru (B) forms a false associatio betwee (A) ad (B), but it is a relatively harmless oe. Whe the associatio is real, however, we have leared somethig valuable about the eviromet from which we ca make predictios that aid i survival ad reproductio. We are the descedats of those who were most successful at fidig patters. This process is called pattericity, or the tedecy to fid meaigful patters i both meaigful ad meaigless oise. The problem is that assessig the differece betwee a Type I ad Type II error is highly problematic especially i the split-secod timig that ofte determies the differece betwee life ad death i our acestral eviromets so the default positio is to assume that all patters are real; that is, assume that all rustles i the grass are dagerous predators ad ot the wid. This is the basis of all superstitio ad magical thikig.
5 11 AGENTICITY, OR SYMPATHETIC MAGIC Let us retur to our homiid o the plais of Africa who hears a rustle i the grass, ad the crucial matter of whether the soud represets a dagerous predator or just the wid: wid represets a iaimate force whereas dagerous predator idicates a itetioal aget. Thus we ted to practice ageticity: the tedecy to ifuse patters with meaig, itetio, ad agecy. That is, we ofte impart the patters we fid with agecy ad itetio, ad believe that these itetioal agets cotrol the world, sometimes ivisibly from the top dow. Souls, spirits, ghosts, gods, demos, agels, alies, ad all maer of ivisible agets with power ad itetio are believed to haut our world ad cotrol our lives. Examples of ageticity aboud. Subjects watchig reflective dots move about i a darkeed room, especially if the dots take o the shape of two legs ad two arms, ifer that they represet a perso or itetioal aget. Childre believe that the su ca thik ad follows them aroud, ad whe asked to draw a picture of the su they ofte add a smiley face to give agecy to it. Geital-shaped foods such as baaas ad oysters are ofte believed to ehace sexual potecy. A third of trasplat patiets believe that the door s persoality or essece is trasplated with the orga. Psychologist Bruce Hood foud that most people say that they would ever wear the sweater of a murderer, showig great disgust at the very thought, as if some of the murderer s evil rubbed off i the material of the sweater, but that most people say that they would wear the cardiga sweater of the childres televisio host Mr. Rogers, believig that wearig the sweater would make them a better perso. We see agecy everywhere we look, ad sometimes those agets are ghosts ad gods, agels ad demos. 12 HYPNOSIS AND MEMORY May alie abductio experieces are remembered years or decades after the fact through a techique called hypotic regressio, i which a subject is hypotized ad asked to imagie regressig back i time to retrieve a memory from the past, ad the play it back o the imagiary scree of the mid, as if there s a dimiutive homuculus sittig iside a little theater i the head ad reportig to the brai s director what he is seeig. This is ot at all how memory works. The metaphor of memory as a videotape playback system is so far off that it is ot eve wrog. There is o recordig device i the brai. Memories are formed as part of the associatio learig system of makig coectios betwee thigs ad evets i the eviromet, ad repetitive associatios betwee them geerates ew coectios betwee euros, which are the stregtheed through additioal repetitio or weakeed through disuse. Use it or lose it. Do you remember your 10th birthday, or do you remember your mother s commets about it as you looked at party photos whe you were 20? Have you added icidets from other parties you atteded or eve party scees from TV? It is likely all of the above, ad much more. So, whe a alie cotactee is recoverig a memory of a abductio experiece, what is actually beig recovered? Aalysis of hypotic regressio tapes used by abductio therapists who employ hyposis shows that they ask leadig questios ad costruct imagiary scearios through which their subjects may cococt a etirely artificial evet of somethig that ever happeed. 13 NEAR-DEATH EXPERIENCES (NDEs) Sice the advet of jet plaes capable of powerful G-force acceleratios that ca cause pilots to lose cosciousess durig aerial maeuvers, the U.S. Air Force ad Navy have udertake a umber of studies o how to fight G-Force Iduced Loss of Cosciousess or G-LOC. Dr. James Whiery studied pilots usig the cetrifuge at the Naval Warfare Ceter i Warmister, PN, where he discovered a remarkable pheomeo experieced by the majority of pilots what he called dreamlets cosistig of brief episodes of tuel visio (sometimes with a bright light at the ed), as well as feeligs of floatig or paralysis, ad, after they regaied cosciousess, a sese of euphoria or peace ad sereity. These are the same characteristics of a Near-Death Experiece (NDE). Whiery iduced NDEs over a thousad times uder the cotrolled coditios of the cetrifuge. Uder high G-Force, the blood drais out of the head ad pools i the torso, sedig pilots first ito a gray-out phase followed by a black-out state, all withi a matter of secods. The NDEs occurred durig black-outs suggestig the cause: apoxia, or oxyge deprivatio to the cortex. Whe G-LOC is iduced i a gradual fashio by acceleratig the cetrifuge i a systematic maer, the subjects first experieced tuel visio, the blidess, the blackout, which is likely caused by the loss of oxyge first to the retia the to the visual cortex (producig tuel visio as the euros shut dow from the outside to the iside), leadig to total blackout whe the majority of the cortex powers dow. NDEs ca also be geerated by electrical stimulatio of the right agular gyrus i the temporal lobe. A 43-year old patiet sufferig from severe epileptic seizures reported feeligs of sikig ito the bed ad fallig from a height after mild electrical stimulatio of this area. More itese stimulatio led her to see [her]self lyig i bed, from above Ad eve more iduced a feelig of lightess ad a sese of floatig about two meters above the bed. The scietists discovered that they could eve cotrol the height above the bed the patiet reported that she floated by the amout of electricity delivered.
6 For more of our famous free dowloads visit skeptic.com: THE SCIENCE BEHIND WHY PEOPLE SEE GHOSTS Do you kow someoe who has had a mid alterig experiece? If so, you kow how compellig they ca be. They are oe of the foudatios of widespread belief i the paraormal. But as skeptics are well aware, acceptig them as reality ca be dagerous TOP 10 THINGS YOU SHOULD KNOW ABOUT ALTERNATIVE MEDICINE BY THE SKEPDOC, HARRIET HALL, M.D. Topics iclude: chiropractic, the placebo effect, homeopathy, acupucture, ad the questioable beefits of orgaic food, detoxificatio, ad atural remedies. WHO BELIEVES THEM? WHY? HOW CAN YOU TELL IF THEY RE TRUE? What is a cospiracy theory, why do people believe i them, ad why do they ted to proliferate? Why does belief i oe cospiracy correlate to belief i others? What are the triggers of belief, ad how does group idetity factor ito it? How ca oe tell the differece betwee a true cospiracy ad a false oe? LEARN TO BE PSYCHIC IN 10 EASY LESSONS TOP 10 MYTHS ABOUT EVOLUTION (AND HOW WE KNOW IT REALLY HAPPENED) If humas came from apes, why are t apes evolvig ito Psychic readigs ad fortuetellig are a aciet art a combiatio of actig ad psychological maipulatio. humas? Fid out i this pamphlet! " YOUR DONATION MATTERS SKEPTICS SOCIETY DONATION CARD Fudraisig, Wie Tastig, Dier, ad Star Parties YES! I d like to support the Skeptics Society i its efforts to ivestigate cotroversial claims & promote sciece & critical thikig. I am eclosig my tax-deductible support i the amout of: $25-$49 $50-$99 $100-$249 $250-$499 $500-$999 $1000 ad above Other $ Please make your check payable to the Skeptics Society. Mail this card to P.O. Box 338, Altadea, CA You may charge your gift by phoig 626/ , or fax the iformatio to 626/ Or doate olie at NAME ADDRESS CITY STATE ZIP PHONE NO. We accept: Accout No. EX. DATE Moth Year Sigature Prit ame EXACTLY as it appears o card The Skeptics Society is a 501(c) (3) oprofit corporatio ad all cotributios are tax deductible. F or doatios of $500 or more you are ivited to joi Michael Shermer i his cliff-side home whe he hosts a fudraisig dier party ad wie tastig evet. We ll have a spectacular suset view of all of Souther Califoria, ad a 8-ich Meade telescope for some star gazig that ight. Dates to be determied. To get o the list to be iformed of upcomig diers ofte with special guests call our office at 626/ Good cause, good fu. Joi us! Michael Shermer, Executive Director, Skeptics Society
Confidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the.
Cofidece Itervals A cofidece iterval is a iterval whose purpose is to estimate a parameter (a umber that could, i theory, be calculated from the populatio, if measuremets were available for the whole populatio).
Professional Networking
Professioal Networkig 1. Lear from people who ve bee where you are. Oe of your best resources for etworkig is alumi from your school. They ve take the classes you have take, they have bee o the job market
In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008
I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces
The Importance of Media in the Classroom
01-TilestoVol09.qxd 8/25/03 3:47 PM Page 1 1 The Importace of Media i the Classroom As teachers, we have a wealth of iformatio from which to choose for our classrooms. We ca ow brig history ito the classroom
Handling. Collection Calls
Hadlig the Collectio Calls We do everythig we ca to stop collectio calls; however, i the early part of our represetatio, you ca expect some of these calls to cotiue. We uderstad that the first few moths
National Institute on Aging. What Is A Nursing Home?
Natioal Istitute o Agig AgePage Nursig Homes: Makig The Right Choice Lucille has lived i her home for 33 years. Eve after her husbad died 3 years ago, she was able to maage o her ow. Recetly, she broke
SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES
SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,
Hypergeometric Distributions
7.4 Hypergeometric Distributios Whe choosig the startig lie-up for a game, a coach obviously has to choose a differet player for each positio. Similarly, whe a uio elects delegates for a covetio or you
G r a d e. 2 M a t h e M a t i c s. statistics and Probability
G r a d e 2 M a t h e M a t i c s statistics ad Probability Grade 2: Statistics (Data Aalysis) (2.SP.1, 2.SP.2) edurig uderstadigs: data ca be collected ad orgaized i a variety of ways. data ca be used
Simple Annuities Present Value.
Simple Auities Preset Value. OBJECTIVES (i) To uderstad the uderlyig priciple of a preset value auity. (ii) To use a CASIO CFX-9850GB PLUS to efficietly compute values associated with preset value auities.
Center, Spread, and Shape in Inference: Claims, Caveats, and Insights
Ceter, Spread, ad Shape i Iferece: Claims, Caveats, ad Isights Dr. Nacy Pfeig (Uiversity of Pittsburgh) AMATYC November 2008 Prelimiary Activities 1. I would like to produce a iterval estimate for the
Hypothesis testing. Null and alternative hypotheses
Hypothesis testig Aother importat use of samplig distributios is to test hypotheses about populatio parameters, e.g. mea, proportio, regressio coefficiets, etc. For example, it is possible to stipulate
THE REGRESSION MODEL IN MATRIX FORM. For simple linear regression, meaning one predictor, the model is. for i = 1, 2, 3,, n
We will cosider the liear regressio model i matrix form. For simple liear regressio, meaig oe predictor, the model is i = + x i + ε i for i =,,,, This model icludes the assumptio that the ε i s are a sample
Pre-Suit Collection Strategies
Pre-Suit Collectio Strategies Writte by Charles PT Phoeix How to Decide Whether to Pursue Collectio Calculatig the Value of Collectio As with ay busiess litigatio, all factors associated with the process
Elementary Theory of Russian Roulette
Elemetary Theory of Russia Roulette -iterestig patters of fractios- Satoshi Hashiba Daisuke Miematsu Ryohei Miyadera Itroductio. Today we are goig to study mathematical theory of Russia roulette. If some
5: Introduction to Estimation
5: Itroductio to Estimatio Cotets Acroyms ad symbols... 1 Statistical iferece... Estimatig µ with cofidece... 3 Samplig distributio of the mea... 3 Cofidece Iterval for μ whe σ is kow before had... 4 Sample
Modified Line Search Method for Global Optimization
Modified Lie Search Method for Global Optimizatio Cria Grosa ad Ajith Abraham Ceter of Excellece for Quatifiable Quality of Service Norwegia Uiversity of Sciece ad Techology Trodheim, Norway {cria, ajith}@q2s.tu.o
Week 3 Conditional probabilities, Bayes formula, WEEK 3 page 1 Expected value of a random variable
Week 3 Coditioal probabilities, Bayes formula, WEEK 3 page 1 Expected value of a radom variable We recall our discussio of 5 card poker hads. Example 13 : a) What is the probability of evet A that a 5
Determining the sample size
Determiig the sample size Oe of the most commo questios ay statisticia gets asked is How large a sample size do I eed? Researchers are ofte surprised to fid out that the aswer depeds o a umber of factors
Lesson 17 Pearson s Correlation Coefficient
Outlie Measures of Relatioships Pearso s Correlatio Coefficiet (r) -types of data -scatter plots -measure of directio -measure of stregth Computatio -covariatio of X ad Y -uique variatio i X ad Y -measurig
Soving Recurrence Relations
Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree
OMG! Excessive Texting Tied to Risky Teen Behaviors
BUSIESS WEEK: EXECUTIVE EALT ovember 09, 2010 OMG! Excessive Textig Tied to Risky Tee Behaviors Kids who sed more tha 120 a day more likely to try drugs, alcohol ad sex, researchers fid TUESDAY, ov. 9
Example 2 Find the square root of 0. The only square root of 0 is 0 (since 0 is not positive or negative, so those choices don t exist here).
BEGINNING ALGEBRA Roots ad Radicals (revised summer, 00 Olso) Packet to Supplemet the Curret Textbook - Part Review of Square Roots & Irratioals (This portio ca be ay time before Part ad should mostly
France caters to innovative companies and offers the best research tax credit in Europe
1/5 The Frech Govermet has three objectives : > improve Frace s fiscal competitiveess > cosolidate R&D activities > make Frace a attractive coutry for iovatio Tax icetives have become a key elemet of public
Domain 1: Designing a SQL Server Instance and a Database Solution
Maual SQL Server 2008 Desig, Optimize ad Maitai (70-450) 1-800-418-6789 Domai 1: Desigig a SQL Server Istace ad a Database Solutio Desigig for CPU, Memory ad Storage Capacity Requiremets Whe desigig a
Repeating Decimals are decimal numbers that have number(s) after the decimal point that repeat in a pattern.
5.5 Fractios ad Decimals Steps for Chagig a Fractio to a Decimal. Simplify the fractio, if possible. 2. Divide the umerator by the deomiator. d d Repeatig Decimals Repeatig Decimals are decimal umbers
Project Deliverables. CS 361, Lecture 28. Outline. Project Deliverables. Administrative. Project Comments
Project Deliverables CS 361, Lecture 28 Jared Saia Uiversity of New Mexico Each Group should tur i oe group project cosistig of: About 6-12 pages of text (ca be loger with appedix) 6-12 figures (please
CHAPTER 3 DIGITAL CODING OF SIGNALS
CHAPTER 3 DIGITAL CODING OF SIGNALS Computers are ofte used to automate the recordig of measuremets. The trasducers ad sigal coditioig circuits produce a voltage sigal that is proportioal to a quatity
Lesson Plans for Teachers
Lesso Plas for Teachers Kidergarte - Grade 3 Copyright 2012 by Little Pickle Press LLC Table of Cotets Quite uique! Streeeetch ad grooow... Overview 3 Activity Set 1 What Is a Brai ad What Does It Do?
Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.
This documet was writte ad copyrighted by Paul Dawkis. Use of this documet ad its olie versio is govered by the Terms ad Coditios of Use located at http://tutorial.math.lamar.edu/terms.asp. The olie versio
How to read A Mutual Fund shareholder report
Ivestor BulletI How to read A Mutual Fud shareholder report The SEC s Office of Ivestor Educatio ad Advocacy is issuig this Ivestor Bulleti to educate idividual ivestors about mutual fud shareholder reports.
Building Blocks Problem Related to Harmonic Series
TMME, vol3, o, p.76 Buildig Blocks Problem Related to Harmoic Series Yutaka Nishiyama Osaka Uiversity of Ecoomics, Japa Abstract: I this discussio I give a eplaatio of the divergece ad covergece of ifiite
I. Chi-squared Distributions
1 M 358K Supplemet to Chapter 23: CHI-SQUARED DISTRIBUTIONS, T-DISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad t-distributios, we first eed to look at aother family of distributios, the chi-squared distributios.
(VCP-310) 1-800-418-6789
Maual VMware Lesso 1: Uderstadig the VMware Product Lie I this lesso, you will first lear what virtualizatio is. Next, you ll explore the products offered by VMware that provide virtualizatio services.
The Forgotten Middle. research readiness results. Executive Summary
The Forgotte Middle Esurig that All Studets Are o Target for College ad Career Readiess before High School Executive Summary Today, college readiess also meas career readiess. While ot every high school
MMQ Problems Solutions with Calculators. Managerial Finance
MMQ Problems Solutios with Calculators Maagerial Fiace 2008 Adrew Hall. MMQ Solutios With Calculators. Page 1 MMQ 1: Suppose Newma s spi lads o the prize of $100 to be collected i exactly 2 years, but
INVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology
Adoptio Date: 4 March 2004 Effective Date: 1 Jue 2004 Retroactive Applicatio: No Public Commet Period: Aug Nov 2002 INVESTMENT PERFORMANCE COUNCIL (IPC) Preface Guidace Statemet o Calculatio Methodology
Amendments to employer debt Regulations
March 2008 Pesios Legal Alert Amedmets to employer debt Regulatios The Govermet has at last issued Regulatios which will amed the law as to employer debts uder s75 Pesios Act 1995. The amedig Regulatios
GCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number.
GCSE STATISTICS You should kow: 1) How to draw a frequecy diagram: e.g. NUMBER TALLY FREQUENCY 1 3 5 ) How to draw a bar chart, a pictogram, ad a pie chart. 3) How to use averages: a) Mea - add up all
Non-life insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring
No-life isurace mathematics Nils F. Haavardsso, Uiversity of Oslo ad DNB Skadeforsikrig Mai issues so far Why does isurace work? How is risk premium defied ad why is it importat? How ca claim frequecy
Lecture 4: Cauchy sequences, Bolzano-Weierstrass, and the Squeeze theorem
Lecture 4: Cauchy sequeces, Bolzao-Weierstrass, ad the Squeeze theorem The purpose of this lecture is more modest tha the previous oes. It is to state certai coditios uder which we are guarateed that limits
Output Analysis (2, Chapters 10 &11 Law)
B. Maddah ENMG 6 Simulatio 05/0/07 Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should
Measures of Spread and Boxplots Discrete Math, Section 9.4
Measures of Spread ad Boxplots Discrete Math, Sectio 9.4 We start with a example: Example 1: Comparig Mea ad Media Compute the mea ad media of each data set: S 1 = {4, 6, 8, 10, 1, 14, 16} S = {4, 7, 9,
CS100: Introduction to Computer Science
Review: History of Computers CS100: Itroductio to Computer Sciece Maiframes Miicomputers Lecture 2: Data Storage -- Bits, their storage ad mai memory Persoal Computers & Workstatios Review: The Role of
Math C067 Sampling Distributions
Math C067 Samplig Distributios Sample Mea ad Sample Proportio Richard Beigel Some time betwee April 16, 2007 ad April 16, 2007 Examples of Samplig A pollster may try to estimate the proportio of voters
How To Solve The Homewor Problem Beautifully
Egieerig 33 eautiful Homewor et 3 of 7 Kuszmar roblem.5.5 large departmet store sells sport shirts i three sizes small, medium, ad large, three patters plaid, prit, ad stripe, ad two sleeve legths log
CS103X: Discrete Structures Homework 4 Solutions
CS103X: Discrete Structures Homewor 4 Solutios Due February 22, 2008 Exercise 1 10 poits. Silico Valley questios: a How may possible six-figure salaries i whole dollar amouts are there that cotai at least
Time Value of Money. First some technical stuff. HP10B II users
Time Value of Moey Basis for the course Power of compoud iterest $3,600 each year ito a 401(k) pla yields $2,390,000 i 40 years First some techical stuff You will use your fiacial calculator i every sigle
.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth
Questio 1: What is a ordiary auity? Let s look at a ordiary auity that is certai ad simple. By this, we mea a auity over a fixed term whose paymet period matches the iterest coversio period. Additioally,
1 Correlation and Regression Analysis
1 Correlatio ad Regressio Aalysis I this sectio we will be ivestigatig the relatioship betwee two cotiuous variable, such as height ad weight, the cocetratio of a ijected drug ad heart rate, or the cosumptio
6. p o s I T I v e r e I n f o r c e M e n T
6. p o s I T I v e r e I f o r c e M e T The way positive reiforcemet is carried out is more importat tha the amout. B.F. Skier We all eed positive reiforcemet. Whether or ot we are cosciously aware of
How to use what you OWN to reduce what you OWE
How to use what you OWN to reduce what you OWE Maulife Oe A Overview Most Caadias maage their fiaces by doig two thigs: 1. Depositig their icome ad other short-term assets ito chequig ad savigs accouts.
Flood Emergency Response Plan
Flood Emergecy Respose Pla This reprit is made available for iformatioal purposes oly i support of the isurace relatioship betwee FM Global ad its cliets. This iformatio does ot chage or supplemet policy
Maximum Likelihood Estimators.
Lecture 2 Maximum Likelihood Estimators. Matlab example. As a motivatio, let us look at oe Matlab example. Let us geerate a radom sample of size 00 from beta distributio Beta(5, 2). We will lear the defiitio
WindWise Education. 2 nd. T ransforming the Energy of Wind into Powerful Minds. editi. A Curriculum for Grades 6 12
WidWise Educatio T rasformig the Eergy of Wid ito Powerful Mids A Curriculum for Grades 6 12 Notice Except for educatioal use by a idividual teacher i a classroom settig this work may ot be reproduced
CS100: Introduction to Computer Science
I-class Exercise: CS100: Itroductio to Computer Sciece What is a flip-flop? What are the properties of flip-flops? Draw a simple flip-flop circuit? Lecture 3: Data Storage -- Mass storage & represetig
A guide to School Employees' Well-Being
A guide to School Employees' Well-Beig Backgroud The public school systems i the Uited States employ more tha 6.7 millio people. This large workforce is charged with oe of the atio s critical tasks to
GOOD PRACTICE CHECKLIST FOR INTERPRETERS WORKING WITH DOMESTIC VIOLENCE SITUATIONS
GOOD PRACTICE CHECKLIST FOR INTERPRETERS WORKING WITH DOMESTIC VIOLENCE SITUATIONS I the sprig of 2008, Stadig Together agaist Domestic Violece carried out a piece of collaborative work o domestic violece
1. C. The formula for the confidence interval for a population mean is: x t, which was
s 1. C. The formula for the cofidece iterval for a populatio mea is: x t, which was based o the sample Mea. So, x is guarateed to be i the iterval you form.. D. Use the rule : p-value
Chapter 6: Variance, the law of large numbers and the Monte-Carlo method
Chapter 6: Variace, the law of large umbers ad the Mote-Carlo method Expected value, variace, ad Chebyshev iequality. If X is a radom variable recall that the expected value of X, E[X] is the average value
AP Calculus AB 2006 Scoring Guidelines Form B
AP Calculus AB 6 Scorig Guidelies Form B The College Board: Coectig Studets to College Success The College Board is a ot-for-profit membership associatio whose missio is to coect studets to college success
5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized?
5.4 Amortizatio Questio 1: How do you fid the preset value of a auity? Questio 2: How is a loa amortized? Questio 3: How do you make a amortizatio table? Oe of the most commo fiacial istrumets a perso
Discrete Mathematics and Probability Theory Spring 2014 Anant Sahai Note 13
EECS 70 Discrete Mathematics ad Probability Theory Sprig 2014 Aat Sahai Note 13 Itroductio At this poit, we have see eough examples that it is worth just takig stock of our model of probability ad may
ABCs. of Diabetes Care
ABCs of Diabetes Care Stayig healthy whe you have diabetes ca be challegig. But the more you focus o the positive results of a healthy diet, medicatio routie ad regular exercise, the easier it will be
15.075 Exam 3. Instructor: Cynthia Rudin TA: Dimitrios Bisias. November 22, 2011
15.075 Exam 3 Istructor: Cythia Rudi TA: Dimitrios Bisias November 22, 2011 Gradig is based o demostratio of coceptual uderstadig, so you eed to show all of your work. Problem 1 A compay makes high-defiitio
Tell us if you need help because of a disability Ask for a free interpreter
Your rights uder Califoria Welfare Programs for people applyig for or receivig public aid i Califoria Tell us if you eed help because of a disability Ask for a free iterpreter 2 Your rights all people
PENSION ANNUITY. Policy Conditions Document reference: PPAS1(7) This is an important document. Please keep it in a safe place.
PENSION ANNUITY Policy Coditios Documet referece: PPAS1(7) This is a importat documet. Please keep it i a safe place. Pesio Auity Policy Coditios Welcome to LV=, ad thak you for choosig our Pesio Auity.
1 Computing the Standard Deviation of Sample Means
Computig the Stadard Deviatio of Sample Meas Quality cotrol charts are based o sample meas ot o idividual values withi a sample. A sample is a group of items, which are cosidered all together for our aalysis.
7.1 Finding Rational Solutions of Polynomial Equations
4 Locker LESSON 7. Fidig Ratioal Solutios of Polyomial Equatios Name Class Date 7. Fidig Ratioal Solutios of Polyomial Equatios Essetial Questio: How do you fid the ratioal roots of a polyomial equatio?
INVESTMENT PERFORMANCE COUNCIL (IPC)
INVESTMENT PEFOMANCE COUNCIL (IPC) INVITATION TO COMMENT: Global Ivestmet Performace Stadards (GIPS ) Guidace Statemet o Calculatio Methodology The Associatio for Ivestmet Maagemet ad esearch (AIM) seeks
Basic Elements of Arithmetic Sequences and Series
MA40S PRE-CALCULUS UNIT G GEOMETRIC SEQUENCES CLASS NOTES (COMPLETED NO NEED TO COPY NOTES FROM OVERHEAD) Basic Elemets of Arithmetic Sequeces ad Series Objective: To establish basic elemets of arithmetic
Listing terms of a finite sequence List all of the terms of each finite sequence. a) a n n 2 for 1 n 5 1 b) a n for 1 n 4 n 2
74 (4 ) Chapter 4 Sequeces ad Series 4. SEQUENCES I this sectio Defiitio Fidig a Formula for the th Term The word sequece is a familiar word. We may speak of a sequece of evets or say that somethig is
Desktop Management. Desktop Management Tools
Desktop Maagemet 9 Desktop Maagemet Tools Mac OS X icludes three desktop maagemet tools that you might fid helpful to work more efficietly ad productively: u Stacks puts expadable folders i the Dock. Clickig
CHAPTER 3 THE TIME VALUE OF MONEY
CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all
To c o m p e t e in t o d a y s r e t a i l e n v i r o n m e n t, y o u n e e d a s i n g l e,
Busiess Itelligece Software for Retail To c o m p e t e i t o d a y s r e t a i l e v i r o m e t, y o u e e d a s i g l e, comprehesive view of your busiess. You have to tur the decisio-makig of your
2-3 The Remainder and Factor Theorems
- The Remaider ad Factor Theorems Factor each polyomial completely usig the give factor ad log divisio 1 x + x x 60; x + So, x + x x 60 = (x + )(x x 15) Factorig the quadratic expressio yields x + x x
5 Boolean Decision Trees (February 11)
5 Boolea Decisio Trees (February 11) 5.1 Graph Coectivity Suppose we are give a udirected graph G, represeted as a boolea adjacecy matrix = (a ij ), where a ij = 1 if ad oly if vertices i ad j are coected
How To Write A Privacy Policy For A Busiess
Office of the Privacy Commissioer of Caada PIPEDA Privacy Guide for Small Busiesses: The Basics Privacy is the best policy Hadlig privacy cocers correctly ca help improve your orgaizatio s reputatio. Whe
Page 1. Real Options for Engineering Systems. What are we up to? Today s agenda. J1: Real Options for Engineering Systems. Richard de Neufville
Real Optios for Egieerig Systems J: Real Optios for Egieerig Systems By (MIT) Stefa Scholtes (CU) Course website: http://msl.mit.edu/cmi/ardet_2002 Stefa Scholtes Judge Istitute of Maagemet, CU Slide What
CS103A Handout 23 Winter 2002 February 22, 2002 Solving Recurrence Relations
CS3A Hadout 3 Witer 00 February, 00 Solvig Recurrece Relatios Itroductio A wide variety of recurrece problems occur i models. Some of these recurrece relatios ca be solved usig iteratio or some other ad
CCH Accountants Starter Pack
CCH Accoutats Starter Pack We may be a bit smaller, but fudametally we re o differet to ay other accoutig practice. Util ow, smaller firms have faced a stark choice: Buy cheaply, kowig that the practice
Baan Service Master Data Management
Baa Service Master Data Maagemet Module Procedure UP069A US Documetiformatio Documet Documet code : UP069A US Documet group : User Documetatio Documet title : Master Data Maagemet Applicatio/Package :
CREATIVE MARKETING PROJECT 2016
CREATIVE MARKETING PROJECT 2016 The Creative Marketig Project is a chapter project that develops i chapter members a aalytical ad creative approach to the marketig process, actively egages chapter members
G r a d e. 5 M a t h e M a t i c s. Number
G r a d e 5 M a t h e M a t i c s Number Grade 5: Number (5.N.1) edurig uderstadigs: the positio of a digit i a umber determies its value. each place value positio is 10 times greater tha the place value
Quadrat Sampling in Population Ecology
Quadrat Samplig i Populatio Ecology Backgroud Estimatig the abudace of orgaisms. Ecology is ofte referred to as the "study of distributio ad abudace". This beig true, we would ofte like to kow how may
Biology 171L Environment and Ecology Lab Lab 2: Descriptive Statistics, Presenting Data and Graphing Relationships
Biology 171L Eviromet ad Ecology Lab Lab : Descriptive Statistics, Presetig Data ad Graphig Relatioships Itroductio Log lists of data are ofte ot very useful for idetifyig geeral treds i the data or the
leasing Solutions We make your Business our Business
if you d like to discover how Bp paribas leasig Solutios Ca help you to achieve your goals please get i touch leasig Solutios We make your Busiess our Busiess We look forward to hearig from you you ca
summary of cover CONTRACT WORKS INSURANCE
1 SUMMARY OF COVER CONTRACT WORKS summary of cover CONTRACT WORKS INSURANCE This documet details the cover we ca provide for our commercial or church policyholders whe udertakig buildig or reovatio works.
INDEPENDENT BUSINESS PLAN EVENT 2016
INDEPENDENT BUSINESS PLAN EVENT 2016 The Idepedet Busiess Pla Evet ivolves the developmet of a comprehesive proposal to start a ew busiess. Ay type of busiess may be used. The Idepedet Busiess Pla Evet
Setting Up a Contract Action Network
CONTRACT ACTION NETWORK Settig Up a Cotract Actio Network This is a guide for local uio reps who wat to set up a iteral actio etwork i their worksites. This etwork cosists of: The local uio represetative,
Two people, one policy. Affordable long-term care coverage for both.
Log-term care rider, available o Natiowide YourLife No-Lapse Guaratee SUL II Feature guide LIFE INSURANCE + LONG-ERM CARE wo people, oe policy. Affordable log-term care coverage for both. NAIONWIDE LIFE
