Question

(i) If a discrete random variable X has a moment generating function M_{X}(t) = frac{e^{-t} + 3 + 4e^{5t}}{10e^{t}} + frac{1}{5}, quad forall t Find the probability mass function of X. (ii) Let X and Y be two independent continuous random variables with moment generating functions M_{X}(t) = frac{1}{sqrt{1 - 2t}} quad ext{and} quad M_{Y}(t) = frac{1}{(1 - 2t)^{3/2}}, quad t < 1/2 Calculate mathbb{E}(X + Y)^{2}

          (i) If a discrete random variable X has a moment generating function
M_{X}(t) = frac{e^{-t} + 3 + 4e^{5t}}{10e^{t}} + frac{1}{5}, quad forall t
Find the probability mass function of X.
(ii) Let X and Y be two independent continuous random variables with moment generating functions
M_{X}(t) = frac{1}{sqrt{1 - 2t}} quad 	ext{and} quad M_{Y}(t) = frac{1}{(1 - 2t)^{3/2}}, quad t < 1/2
Calculate mathbb{E}(X + Y)^{2}

$(i) If a discrete random variable X has a moment generating function MX(t) = frace^-t + 3 + 4e^5t10e^t + frac15, quad forall t Find the probability mass function of X. (ii) Let X and Y be two independent continuous random variables with moment generating functions MX(t) = frac1sqrt1 - 2t quad extand quad MY(t) = frac1(1 - 2t)^3/2, quad t < 1/2 Calculate mathbbE(X + Y)^2$

Added by Robert J.

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