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Lecture16(10-01-2008) - 36-225 Handout for Lecture 16...

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36-225 - Handout for Lecture # 16 October 1, 2008 Special Discrete Random Variables - Review I. The Binomial Random Variable – X Bin( n, p ). X counts the number of successes out of n independent (Bernoulli) trials, each having a probability of “success” p . II. The Geometric Random Variable – X Geom( p ). Consider a series of independent (Bernoulli) trials, each having probability of “success” p . X is the number of trials until the first “success”. Comment: The geometric random variable is the only discrete random variable that has the memoryless property: P ( X > a + b | X > a ) = P ( X > b ). III. The Negative Binomial Random Variable – X NB( r, p ). Consider a series of independent (Bernoulli) trials, each having probability of “success” p . X is the number of trials until we get r “successes”. Clearly, NB(1 , p ) is the same as Geom( p ). IV. The Hypergeometric Random Variable – X HG( n, N, r ). A sample of size n is chosen (without replacement) from a group of size N that has r “successes” (and N - r “failures”). X is the number “successes” in the sample.
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