Statistics Class 10 2/29/2012

Transcription

1 Statistics Class 10 2/29/2012

2 Quiz 8 When playing roulette at the Bellagio casino in Las Vegas, a gambler is trying to decide whether to bet $5 on the number 13 or to bet $5 that the outcome is any one of these five possibilities: 0 or 00 or 1 or 2 or 3. From Example 8, we know that the expected value of the $5 bet for a single number is -26. For the $5 bet that the outcome is 0 or 00 or 1 or 2 or 3, there is a probability of 5/38 of making a net profit of $30 and a 33/38 probability of losing $5. a. Find the expected value for the $5 bett that the outcome is 0 or 00 or 1 or 2 or 3. b. Which bet is better: A $5 bet on the number 13 or a $5 bet that the outcome is 0 or 00 or 1 or 2 or 3? Why?

3 A binomial probability distribution results from a procedure that meets all the following requirements.

4 A binomial probability distribution results from a procedure that meets all the following requirements. 1. The procedure has a fixed number of trials.

5 A binomial probability distribution results from a procedure that meets all the following requirements. 1. The procedure has a fixed number of trials. 2. The trials must be independent. (The outcome of any individual trial doesn t affect the probabilities in the other trials.)

6 A binomial probability distribution results from a procedure that meets all the following requirements. 1. The procedure has a fixed number of trials. 2. The trials must be independent. (The outcome of any individual trial doesn t affect the probabilities in the other trials.) 3. Each trial must have all outcomes classified into two categories (commonly referred to as success and failure).

7 A binomial probability distribution results from a procedure that meets all the following requirements. 1. The procedure has a fixed number of trials. 2. The trials must be independent. (The outcome of any individual trial doesn t affect the probabilities in the other trials.) 3. Each trial must have all outcomes classified into two categories (commonly referred to as success and failure). 4. The probability of a success remains the same in all trials.

8 Note on Independence Often when selecting a sample we do so without replacement. This means that our events are dependent, and violate rule 2 of the binomial probability distribution. However we can use the 5% guideline for cumbersome calculations, and treat dependent events independent as long as the sample size is no more than 5% of the population size.

9 Notation for a Binomial Probability Distribution S and F (success and failure) denote the two possible categories of outcomes.

10 Notation for a Binomial Probability Distribution S and F (success and failure) denote the two possible categories of outcomes. P(S)=p p=probability of success)

11 Notation for a Binomial Probability Distribution S and F (success and failure) denote the two possible categories of outcomes. P(S)=p p=probability of success) P(F)=q q=probability of failure)

12 Notation for a Binomial Probability Distribution S and F (success and failure) denote the two possible categories of outcomes. P(S)=p p=probability of success) P(F)=q q=probability of failure) n denotes the fixed number of trials

13 Notation for a Binomial Probability Distribution S and F (success and failure) denote the two possible categories of outcomes. P(S)=p p=probability of success) P(F)=q q=probability of failure) n denotes the fixed number of trials x denotes a specific number of successes in n trials

14 Notation for a Binomial Probability Distribution S and F (success and failure) denote the two possible categories of outcomes. P(S)=p p=probability of success) P(F)=q q=probability of failure) n denotes the fixed number of trials x denotes a specific number of successes in n trials p denotes the probability of success in one of the n trials

15 Notation for a Binomial Probability Distribution S and F (success and failure) denote the two possible categories of outcomes. P(S)=p p=probability of success) P(F)=q q=probability of failure) n denotes the fixed number of trials x denotes a specific number of successes in n trials p denotes the probability of success in one of the n trials q denotes the probability of failure in one of the n trials

16 Notation for a Binomial Probability Distribution S and F (success and failure) denote the two possible categories of outcomes. P(S)=p p=probability of success) P(F)=q q=probability of failure) n denotes the fixed number of trials x denotes a specific number of successes in n trials p denotes the probability of success in one of the n trials q denotes the probability of failure in one of the n trials P(x) denotes the probability of getting exactly x successes among the n trials

17 Lets look at example 1 on page 220, then do problem 1 on the worksheet!

18 Binomial Probability Formula In a binomial Probability distribution, probabilities can be calculated by using the binomial probability formula.

19 Binomial Probability Formula In a binomial Probability distribution, probabilities can be calculated by using the binomial probability formula. First recall/learn: Factorial symbol (!) denotes the product of decreasing powers of positive whole numbers.

20 Binomial Probability Formula In a binomial Probability distribution, probabilities can be calculated by using the binomial probability formula. First recall/learn: Factorial symbol (!) denotes the product of decreasing powers of positive whole numbers. So 4! = and 0! = 1.

21 Binomial Probability Formula In a binomial Probability distribution, probabilities can be calculated by using the binomial probability formula. First recall/learn: Factorial symbol (!) denotes the product of decreasing powers of positive whole numbers. So 4! = and 0! = 1. where n=number of trials P x = n! n x!x! px q n x for x = 0,1,2,, n x=number of success among n trials (p=probability of success/q=probability of failure) in any one trial

22 We are going to do example 3 three times! 1 st by hand, 2 nd by excel, and 3 rd by table.

23 We are going to do example 3 three times! 1 st by hand, 2 nd by excel, and 3 rd by table. Now do problems 2, 3, and 4 on the worksheet.

24 μ, σ 2, and σ for Binomial Distributions Recall for a probability distribution that; μ = [x P(x)]

25 μ, σ 2, and σ for Binomial Distributions For a Binomial Distribution μ, σ 2, and σ are given by the following formulas:

26 μ, σ 2, and σ for Binomial Distributions For a Binomial Distribution μ, σ 2, and σ are given by the following formulas: μ = n p

27 μ, σ 2, and σ for Binomial Distributions For a Binomial Distribution μ, σ 2, and σ are given by the following formulas: μ = n p σ 2 = n p q

28 μ, σ 2, and σ for Binomial Distributions For a Binomial Distribution μ, σ 2, and σ are given by the following formulas: μ = n p σ 2 = n p q σ = n p q

29 μ, σ 2, and σ for Binomial Distributions For a Binomial Distribution μ, σ 2, and σ are given by the following formulas: μ = n p σ 2 = n p q σ = n p q Now lets do example 1 and 2, then do problem 6 on the worksheet

30 Homework!!! 5-3: 1-8,13, 33, 35, and : 1-12, 19