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Unformatted text preview: are independent. ,0<x 1 <1; zero elsewhere ,0<x 2 <1; zero elsewhere Since , so the random variables X1 and X2 are independent. 4) One cookie in 5 is broken. If 20 are grabbed, what are (a) P(4 broken), (b) P(at most 2 broken), and (c) P(at least 4 broken)? Answer: The situation is analogous to a succession of Bernoulli trails, with a broken cookie corresponding to a success. Let X be the number of broken cookies. Hence p=1/5, q=1-p=4/5, and n=20. Consequently, a) P(4 broken) = P(X=4) = = 0.2182 b) P(at most 2 broken) = P(X= 0 or 1 or 2) = = 0.2061 c) P(at least 4 broken) = 1 – P(X<4) = 1 – ( P(X=0) +P(X=1) +P(X=2) +P(X=3) ) = = 0.5886...
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- Spring '12
- Variance, Probability theory, probability density function, X1 given X2, X2 given X1