quantities. (a) Let A and B be independent events with P[A] = 1/5 and P[B] =...
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quantities. (a) Let A and B be independent events with P[A] = 1/5 and P[B] = 1/4. Calculate P[An B] and P[AU B]. = (b) Let A₁, A2, A3 be events that are conditionally independent given B. Additionally, assume that A₁, A2, A3 are conditionally independent given Bc. Assume that P[A;|B] = 1/4 and P[A, B] = 1/2 for i 1, 2, 3 and P[B] = 1/3. Calculate P[A1₁ÑæÑA3|B] and P[A₁A₂A3]. (c) Consider a packet of jellybeans that contains 9 jellybeans, of which 4 are lemon and the remaining 5 are raspberry. You reach in and pull out 3 jellybeans. What is the probability that they are all lemon? What is the probability that they are all raspberry? (d) Let X be a random variable with PMF Px(x): and P[X>0|X #0]. (e) If the random variable Y has CDF Fy (y) Calculate each of the requested = (1/6 x = -1, +1 2/3 x=0 Calculate P[X # 0] y < 1 1/4 1≤y < 5, what is the PMF of Y? 5 ≤y quantities. (a) Let A and B be independent events with P[A] = 1/5 and P[B] = 1/4. Calculate P[An B] and P[AU B]. = (b) Let A₁, A2, A3 be events that are conditionally independent given B. Additionally, assume that A₁, A2, A3 are conditionally independent given Bc. Assume that P[A;|B] = 1/4 and P[A, B] = 1/2 for i 1, 2, 3 and P[B] = 1/3. Calculate P[A1₁ÑæÑA3|B] and P[A₁A₂A3]. (c) Consider a packet of jellybeans that contains 9 jellybeans, of which 4 are lemon and the remaining 5 are raspberry. You reach in and pull out 3 jellybeans. What is the probability that they are all lemon? What is the probability that they are all raspberry? (d) Let X be a random variable with PMF Px(x): and P[X>0|X #0]. (e) If the random variable Y has CDF Fy (y) Calculate each of the requested = (1/6 x = -1, +1 2/3 x=0 Calculate P[X # 0] y < 1 1/4 1≤y < 5, what is the PMF of Y? 5 ≤y
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Related Book For
Finite Mathematics and Its Applications
ISBN: 978-0134768632
12th edition
Authors: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair
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