Transcript 6.3 Geometric

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* 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
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*The four conditions for a binomial setting
are:
1.
2.
3.
4.
Success/Failure
Independent Trials
Constant “p” (probability of success)
No set number of trials, n
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* 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, ….
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* 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?
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* 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,
𝑃 𝑌 = 𝑘 = (1 − 𝑝)𝑘−1 𝑝
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* Find the probability that it takes 3 turns to roll
doubles and get out of jail.
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* Find the probability that it takes more than 3
turns to roll doubles, and interpret this value
in context.
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* If Y is a geometric random variable with
probability of success p on each trial, then its
1
mean (expected value) is 𝐸 𝑌 = 𝜇𝑌 =
𝑝
* In other words, the expected number of trials
required to get the first success is
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1
𝑝
* There is a formula for standard deviation, but…
* 𝜎𝑌 =
1−𝑝
𝑝2
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* Same homework assignment as yesterday…just
keep working on it!
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