The two-parameter exponential distribution uses a different range for the random variable X, namely, 0 ≤ γ ≤ x for a constant γ (and this equals the usual exponential distribution in the special case that γ = 0). The probability density function for X is f (x) = λexp[−λ(x − γ )] for 0 ≤ γ ≤ x and 0 < λ. Determine the following in terms of the parameters λ and γ : 

(a) Mean and variance of X. 

(b) P(X < γ +1/ λ)