Geometric Distribution In some situations, the critical quantity is the WAITING TIME (Waiting...

Geometric DistributionIn some situations, the critical quantity is the WAITING TIME (Waiting period) number of trials before a specific outcome (success) occurs has only two outcomes, success or failure the difference is the waiting time, the number of failure trials before success occurs.

Apply the product rule to find the probability of successive independent events. Each unsuccessful event adds another factor to the probability, making it look likeP(x) = qxp, where p and q are the same as we know them.

Expectations for a Geometric DistributionE(x) = = but this expectation converges to a simple formula.

0

)(x

xxPp

q

If we are looking for the amount of time before a failure occurs, a success is actually failing something, which means that p becomes q, and q becomes p.

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

Remember: there are 5 days in a school week, therefore we need to look at P(0 < x < 4)

Why did we add?

HomeworkPg 394 # 1,3,6,7