Let X a random variable that follows Gamma with parameters a=1 and b=2. That is fX (x) = xe(−x). Let a function g(x)= 10 if 0<x<3 and 3+4(x-2) if x>3. Then calculate the mean value of g(x). I suppose that i have take the integral of the g(x) from 0 to 3 of 10*f(x) and integral from 3 to infinity of [3+4(x-2)]*f(x) and then i will come up with E[X|X>3]. Is that correct? If yes is there any way to calculate the integral of x^{2}exp{-x} 'faster' than analyticaly? Thanks
Hi Idk I don't recognise that question from the course notes or IFOA, so please share a reference if you have one. Did you mean a Gamma(2,1)? 'I suppose that i have take the integral of the g(x) from 0 to 3 of 10*f(x) and integral from 3 to infinity of [3+4(x-2)]*f(x)' Yes, your integrals are correct, generally you want the integral of g(x)*fX(x) dx for all values of x, and this will give you the E[g(X)]. Generally, I would integrate 'x^{2}exp{-x}' by parts. Andrea
