Question: 2. Let X be a random variable with probability density function f (x) = 1/4 if x (1, 3) 0 otherwise.

2. Let X be a random variable with probability density function f (x) =    1/4 if x ∈ (−1, 3) 0 otherwise.

(a) Find MX(t), E(X), and Var(X).

(b) Using MX(t), calculate E(X). Hint: Note that by the definition of derivative, M7 X(0) = lim h→0 MX(h) − MX(0) h .

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