Question: Please answer in detail, I will give thumbs up. Let X be a discrete random variable taking values from N with the following PMF (probability

Please answer in detail, I will give thumbs up.

Let X be a discrete random variable taking values from N with the following PMF (probability mass function), 0.1 k =1 0.2 k = 2 P( X = k) = 0.3 k = 3 (1) 0.4 k =4 0 otherwise (a) Calculate E(X ) and V(X). (b) If Y = X(X - 1), calculate E( Y). (c) Prove that E(X) = _. P(X

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