1.) Let Y be a discrete random variable with probability mass function (pmf) given by: y 1 2 3 4 P(Y=y) 0.1 a 0.2 0.5 i.) Determine the value of a [2] ii.) Find the cumulative distribution function (cdf) of Y. [1] iii.) Determine the following: a.) P(Y < 3) [1] b.) E(Y) [2] c.) E(2Y - 2) [2] d.) Var(Y) [2] 2.) Let X be a discrete random variable with probability mass function (pmf) given by: x 1 2 3 4 P(X=x) 0.2 0.3 0.4 0.1 Determine the following: a.) P(X ? 3) [1] b.) P(2 ? X ? 4) [1] c.) E(X) [2] d.) E(X + 1) [2] e.) Var(X) [2] f.) Var(X + 1) [2]
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) Let Y be a discrete random variable with probability mass function (pmf) given by: P(Y = y) = {0.1a, 0.2a, 0.3a} for y = {2, 3, 5} i.) Determine the value of a [2] Since the sum of all probabilities in a pmf must equal 1, we have: 0.1a + 0.2a + 0.3a = 1 0.6a = Show more…
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