Geometric Distribution. Similar to Binomial Similar to Binomial Success/FailureSuccess/Failure Probabilities do NOT changeProbabilities do NOT change.

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Presentation transcript:

Geometric Distribution

Similar to Binomial Similar to Binomial Success/FailureSuccess/Failure Probabilities do NOT changeProbabilities do NOT change Now you are looking at the number of failures until a success. Now you are looking at the number of failures until a success. Determining the prob2ity that you will have to wait for a certain amount of time before an event occurs Determining the prob2ity that you will have to wait for a certain amount of time before an event occurs

Probability and Expectation for Geometric Distribution Where p is the probability of a success in each single trial and q is the probability of a failure Where p is the probability of a success in each single trial and q is the probability of a failure The expectation converges to a simple formula The expectation converges to a simple formula

Ex Jamaal has a success rate of 68% for scoring on free throws in basketball. What is the expected waiting time before he misses the basket on a free throw? The random variable is the number of trials before he misses a free throw A success is Jamaal failing to score q=0.68p=1-0.68=0.32

Ex Suppose that an intersection you pass on your way to school has a traffic light that is green 40 s and then amber or red for a total of 60s a) What is the probability that the light will be green when you reach the intersection at least once a week? b) What is the expected number of days before the light is green when you reach the intersection?

a) What is the probability that the light will be green when you reach the intersection at least once a week? p= light is green = 40/100 = 0.40 q= light not green = 60/100 = 0.60 There are 5 school days so we want the probability that you will wait 0 days, 1 day, 2 days, 3 days or 4 days before it is green

b) What is the expected number of days before the light is green when you reach the intersection? The expected waiting time before catching a green light is 1.5 days

Homework! Pg 394 #1,2,3,7,9,10