Question: Consider the following PMF for a random variable X: p(4) = 0.3, p(2) = 0.15, p(0) = 0.1, p(2) = 0.15, p(4) = 0.3 a)

Consider the following PMF for a random variable X: p(4) = 0.3, p(2) = 0.15, p(0) = 0.1, p(2) = 0.15, p(4) = 0.3

a) Is this a legitimate PMF? Explain why or why not.

b) Calculate E(X).

c) Calculate Var(X).

d) Suppose Y=2X+1. Determine E(Y) and Var(Y).

e) Calculate 2E(X)+1. Is this equal to E(Y)? Explain why or why not

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