AP Statistics Notes Chapter 6 - Discrete, Binomial, and Geometric Random Variables

probability of success

The ________- call it p- remains the same for each observation.

probability distribution of X

The ________ lists the values and their probabilities.

variable of interest

The ________ is the number of trials required to obtain the first success.

pk The probabilities pi must satisfy two requirements

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6.3

The Binomial Distributions A binomial probability distribution occurs when the following requirements are met

Each observation falls into one of just two categories

call them "success" or "failure."

The procedure has a fixed number of trials

we call this value n. 3

The observations must be independent

result of one does not affect another

The probability of success

call it p -remains the same for each observation

Notation for binomial probability distribution n denotes the number of fixed trials k denotes the number of successes in the n trials p denotes the probability of success 1

p denotes the probability of failure

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binomcdf(n, p, k)

P(X  3) = 1

binomcdf(4, .8, 3)

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binomcdf(n, p, k -1)

For n = 4, p = .8,   (4)(.8)  3.2 , which means we expect 3.2 makes out of 4 shots, on average 6.3

The Geometric Distributions A geometric probability distribution occurs when the following requirements are met

Each observation falls into one of just two categories

call them "success" or "failure."

The observations must be independent

result of one does not affect another

The probability of success

call it p -remains the same for each observation

As such, the geometric is also called a "waiting-time" distribution Notation for geometric probability distribution n denotes the number of trials required to obtain the first success p denotes the probability of success 1

p denotes the probability of failure

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geometcdf(p, n)

P(X  3) = 1

geometcdf(.8, 3)

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geometcdf(p, n-1)

P(X  3)= 1

geometcdf( .8, 2) Mean (expected value) of a Geometric Random Variable