Question: The distribution of a continuous Random Variable X is as follows. f(x) = (k) * (x^2) * e^(-x), where x>0. 1) Find the value of

The distribution of a continuous Random Variable X is as follows. f(x) = (k) * (x^2) * e^(-x), where x>0.

1) Find the value of k.

2) Compute MGF of X, E[X], Var[X]

3) We need the distribution of Y = e^(-X).

4) Derive its PDF, h(y)

5) Find E(Y) using f(x) and h(y)

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