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Unformatted text preview: 36-225 - Handout for Lectures # 13 & 14September 24 & 26, 2008Special Discrete Random Variables (Distributions)I. The Binomial Random Variable (Distribution)Consider an experiment which consists of n independent (Bernoulli) trials, each hav-ing two possible outcomes (Success or Failure), and each having P(Success) =p.Let the RV Y be the number of successes (out of n).Y is said to be a binomial random variable, and we write:PY(y) =P(Y=y) =nypy(1-p)n-yy=1,2, . . . ,nE(Y) =npV(Y) =np(1-p)II. The Geometric Random Variable (Distribution)Consider asequenceof independent Bernoulli trials, all having the same P(Success)=p.Define:Y - the number of trials until the first success.We say thatYis ageometricrandom variable, and we write:Example: Toss a fair coin repeatedly, and letYbe the number of tosses (trials) untilthe first H.=YGeom(p= 1/2).IfYGeom(p), what is the probability distribution ofY,PY(y)?...
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