I need help. The problem is this:
X is an exponentially distributed random variable with p.d.f.
Show that the m.g.f. of X is for , and use this to find E(X) and Var(X).
I have no idea what to do with this problem or where to start. Please help point me somewhere? The only thing I could think of to potentially do is to undo the p.d.f. to get the original random variable, but...yeah. I'm really, really lost.
Let X and Y be two Statistically independent Exponentially distributive random variables with parameters and respectively.
a) find the CDF (commulative density function) of Z = X/X+Y , (use property of exponential pdf to evaluate the integrals in this question).
b) find the expected value of Z when =1, and = 2
So please can any one solve this, with all the steps of integration , Thanks a lot.