4.12 The Geometric Distribution

Identifying the difference between binomial and geometric random variables is important. The main difference between them is that binomial random variables have fixed trials but geometric random variables do not. 

A ⭕️geometric setting arises when we perform independent trials of the same chance process and record the number of trials it takes to get one success. On each trial, the probability p of success must be the same. The number of trials Y that it takes to get one success in a geometric setting is a geometric random variable. The probability distribution of Y is a geometric distribution with probability p of success on any trial. The possible values of Y are 1, 2, 3, … n. 

Calculating Probabilities 

If Y has the geometric distribution with probability p of success on each trial, then the possible values of Y are 1, 2, 3, … if k is one of these values then you can use the Geometric probability formula: P(Y=k) = (1-p)^k-1 (p) . You can use geometricCDF or geometricPDF to calculate probabilities. 

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Shape, Center, and Variability

To find the mean and standard deviation of a geometric distribution, use the following formulae: 

Mean Y= 1/p ,where p is the probability of success. 

Standard Deviation Y= Sqrt((1-p)/p), where p is the probability of success.

Every geometric distribution has a skewed right graph.

🎥Watch: AP Stats - Probability: Random Variables, Binomial/Geometric Distributions

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