Let X 1 , X 2 , . . . , X n be n independent gamma random variables with parameters (r 1 , λ), (r 2 , λ), ... , (r n , λ), respectively. Use moment-generating functions to find the probability...

Let X₁, X₂, . . . , X_n
be n independent gamma random variables with parameters (r₁, λ), (r₂, λ), ... , (r_n, λ), respectively. Use moment-generating functions to find the probability distribution function of X₁
+ X₂
+ · · · + X_n.