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Unformatted text preview: k = 0 , 1 , 2 , 3 with n = 10 and p = 0 . 1; n = 20 and p = 0 . 05; n = 100 and p = 0 . 01. 7. Let X denote the number of hours a student studies during a randomly selected day. Suppose the probability law is speciﬁed by the cdf given by F ( x ) = , x < 1 8 x + 1 8 , ≤ x < 1 1 2 , 1 ≤ x < 2 1 8 x + 1 2 , 2 ≤ x < 4 1 , x ≥ 4 . a. Sketch the cdf. b. Find the probability that the student: (i) studies exactly 2 hours; P ( X = 2) (ii) studies exactly 3 hours; P ( X = 3) (iii) studies; that is, P ( X > 0) (iv) studies more than 2 hours; P ( X > 2) (v) studies less than 2 hours; P ( X < 2) (vi) studies between 1 and 3 hours; P (1 < X < 3) (vii) studies more than 2 hours given that he does study; P (2 < X  X > 0) (viii) studies less than 3 hours given that he studies more than 1 hour; P ( X < 3  X > 1). 2...
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 Spring '08
 LORENZELLI
 Probability theory, Binomial distribution, Randomness, Cumulative distribution function, 16th Read LeonGarcia

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