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17 Binomial Distribution Xv # 0‘0 5155955 111 ”a 5
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a The Binomial distribution and random variable occur when modeling n xrfhferent trials
of Bernoulli trials, Suppose an experiment consists of 21 sequence of 71 smaller (yet
similar) experiments called trials, the 77, trials are ﬁxed. Suppose each trial results
in one of the same two distinct outcomes (dichotomousj disjoint). Suppose the trials
are independent, one trial does not depend nor inﬂuence another trial. Suppose the
probability of success is the same for each trialI p, X N 13mm, p). , Reliability: pass or fail for many objects or components 7* Package Routing: left or right in each node of the route I Let X represent the number of successes in 7; trials each with probability of succese 210 The pm‘f of X is given by PCX—b): PGCFP):
P(X : 1:} : ( 2 )f {1 719)“ 396(an FnU l9)“ : ﬂ? (1—Pln ”IQ=0, =71l  The mean is given by ELY] : p. : up, the variance is given by Varpg = r72 : npﬂwp)
A“ l, 9 Example: Suppose that 20% of all copies of your textbook fail a certain binding
strength test. Let X be the number of among 15 randomlv Sampled books that fail the test. X/‘L/ 61"“ng Ptgpj EEK] ‘l’\ (7 15L 9): 3 (a) \Vhet is the average number of copies that fail the test? Eta: n F = “50162):3 e1 1001 a
(b) What is the variance of the number of copies that fail the test? vain]: were): 2H iexr me (e) lVhat is the probability that zero copies fail the test? Peso): [QCJOYWDDM = 0.035 23.5% ...
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 Fall '07
 Carlton

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