*Homework Questions

*Section 6.3Geometric Random Variables

*Examples of Geometric

*Roll a pair of dice until you get doubles

*In basketball, attempt a three-point shot until you make one

*Keep placing $1 bets on the number 15 in roulette until you win

*Geometric Setting

*The four conditions for a binomial setting are:

1. Success/Failure

2. Independent Trials

3. Constant “p” (probability of success)

4. No set number of trials, n

*Geometric Random Variable and Geometric

Distribution

*The number of trials Y that it takes to get a success in a geometric setting is a geometric random variable. The probability distribution of Y is a geometric distribution with parameter p, the probability of a success on any trial. The possible values of Y are 1, 2, 3, ….

*Monolopy

*In Monopoly, one way to get out of jail is to roll doubles. How likely is it that someone in jail would roll doubles on his first, second, or third attempt? If this was the only way to get out of jail, how many turns would it take, on average?

*Geometric Probability

*If Y has the geometric distribution with probability p of success on each trial, the possible values of Y are 1, 2, 3,… If k is any one of these values,

*Monopoly

*Find the probability that it takes 3 turns to roll doubles and get out of jail.

*Monopoly

*Find the probability that it takes more than 3 turns to roll doubles, and interpret this value in context.

*Mean of Geometric

Random Variable

*If Y is a geometric random variable with probability of success p on each trial, then its mean (expected value) is

*In other words, the expected number of trials required to get the first success is

*Standard Deviation

*There is a formula for standard deviation, but…

*Homework

*Same homework assignment as yesterday…just keep working on it!