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Unformatted text preview: 36-225 - Handout for Lecture # 16October 1, 2008Special Discrete Random Variables - ReviewI.The Binomial Random Variable XBin(n, p).Xcounts the number of successes out ofnindependent (Bernoulli) trials, each having a probabilityof successp.II.The Geometric Random Variable XGeom(p).Consider a series of independent (Bernoulli) trials, each having probability of successp.Xis the number of trials until thefirstsuccess.Comment:The geometric random variable is the only discrete random variable that has thememoryless property:P(X > a+b|X > a) =P(X > b).III.The Negative Binomial Random Variable XNB(r, p).Consider a series of independent (Bernoulli) trials, each having probability of successp.Xis the number of trials until we getrsuccesses.Clearly, NB(1, p) is the same as Geom(p).IV.The Hypergeometric Random Variable XHG(n, N, r).A sample of sizenis chosen (without replacement) from a group of sizeNthat hasrsuccesses(andN-rfailures).Xis the number successes in the sample.Comment:WhenN >20nthenHG(n, N, r)Bin(n,rN)V.The Poisson Random Variable XPoisson()....
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