I am given a continuous random variable F which is the sum of 3 exponential distributed random variables X, Y, and Z. The parameter of X isλ and the parameter for Y and Z isμ.

X, Y and X, Z are independent, and the correlation between Y and Z is B. I am told to obtain the first 2 moments of F. How would I go about solving this problem?

I know to find the moments for a random variable is E[x^n]=n!/λ^n.