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Understanding Binomial and Geometric Random Variables in AP Statistics

This resource delves into binomial and geometric random variables, specifically in a binary setting involving independent trials of the same chance process. It outlines the four essential conditions for a binomial setting: binary outcomes (success or failure), independence of trials, a fixed number of trials (n), and a constant probability of success (p) across trials. The binomial distribution is defined, along with the concept of a binomial random variable, which counts the number of successes in fixed trials. The factorial and binomial coefficient are also discussed, providing a comprehensive understanding of these statistical concepts.

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Understanding Binomial and Geometric Random Variables in AP Statistics

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  1. AP Statistics Notes Chapter 6- Section 6.3Binomial and Geometric Random Variables

  2. Binary Setting- Arises when we perform several independent trials of the same chance process and record the number of times that a particular outcome occurs.

  3. 4 Conditions for a Binomial Setting B inary? The possible outcomes of each trial can be classified as “success” or “failure” I ndependent? Trials must be independent; knowing the result of one trial must not have any effect on the result of any other trial N umber? The number of trials n of the chance process must be fixed in advance S uccess? On each trial, the probability p of success must be the same

  4. When checking the Binary condition, there can be more than 2 possible outcomes per trial but you can define one thing as “success” so it either is (success) or isn’t (failure)

  5. Binomial Random Variable- Count of X successes in a binomial setting Binomial Distribution- Probability distribution of X with parameters n and p, where n is the number of trials of the chance process and p is the probability of a success on any 1 trial. The possible values of X are the whole numbers from 0 to n.

  6. Factorial- n! = n(n – 1)(n – 2)…. (3)(2)(1) for any positive whole number n Binomial Coefficient- Number of ways of arranging k successes among n observations is given by: ( ) n k _ n!___k! (n – k)! =

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