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a) let X follow the probability density function f(x):=e^(-x) if x>0, if Y is an independent...

a) let X follow the probability density function f(x):=e^(-x) if x>0, if Y is an independent random variable following an identical distribution f(x):=e^(-x) if x>0, calculate the moment generating function of 2X+3Y

b) If X follows a bernoulli(0.5), and Y follows a Binomial(3,0.5), and if X and Y are independent, calculate the probability P(X+Y=3) and P(X=0|X+Y=3)

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