5. A random variable X= {0, 1, 2, 3, ...} has cumulative distribution function F(x) = P(X ≤ x) = 1 - (x+1)(x+2) a) Calculate the probability that 3 ≤X≤5. b) Find the expected value of X, E(X), using the fact that E(X) = Evo[1 F(Y)]. (Hint: You will have to evaluate an infinite sum, but that will be easy to do if you notice that (x+1)(x+2) = (x+1) (x+2)

5. A random variable X= {0, 1, 2, 3, ...} has cumulative distribution function F(x) = P(X ≤ x) = 1 - (x+1)(x+2) a) Calculate the probability that 3 ≤X≤5. b) Find the expected value of X, E(X), using the fact that E(X) = Evo[1 F(Y)]. (Hint: You will have to evaluate an infinite sum, but that will be easy to do if you notice that (x+1)(x+2) = (x+1) (x+2)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 35E

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