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Pg 36 - -— l 1 WM ever went:9 WP" 91 mBerCP ~P,2 Cam...

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Unformatted text preview: -—-_ l 1 WM ever) went :9 WP" 91} mBerCP) ~P ,2) Cam! lam-j 1 ~ . ”we are” 5:2 w v , ‘11 W 1 n w 1 17 Binomial Distribution Xv # 0‘0 5155955 111 ”a 5 X: )(i 7LK1'} ‘ ' +D< 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 21-0 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) l-Vhat is the probability that zero copies fail the test? Peso): [QCJOYWDDM =- 0.035 23.5% ...
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