ap stats study guides

โœŒ๏ธย  Unit 2 - Exploring Two-Variable Data

โš–๏ธย  Unit 6 - Inference for Categorical Data: Proportions

๐Ÿ˜ผย  Unit 7 - Inference for Qualitative Data: Means

โœณ๏ธย  Unit 8 Inference for Categorical Data: Chi-Square

๐Ÿ“ˆย  Unit 9 - Inference for Quantitative Data: Slopes

๐Ÿงย  Multiple Choice Questions (MCQs)

4.12 The Geometric Distribution

#statisticalinference

#exploringdata

โฑ๏ธย ย 2 min read

written by

kanya shah


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.ย 

A โญ•๏ธ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, โ€ฆ n.ย 

Calculating Probabilitiesย 

If Y has the geometric distribution with probability p of success on each trial, then the possible values of Y are 1, 2, 3, โ€ฆ 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.ย 

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Shape, Center, and Variability

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

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

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

Every geometric distribution has a skewed right graph.

๐ŸŽฅWatch: AP Stats - Probability: Random Variables, Binomial/Geometric Distributions

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