Consider an RV X with the following density given parameters α and γ .

Question

f (x) = {(1/γ)e^(-(x-α)/γ) if x>α
{0 if x ≤ α.
a. Find E[X].
b. Find V[X].
c. If α = 4, γ = 2, find P (X > 8).
d. Find P (X < α + 3γ ).
e. Find the cdf for X , F (x).