expected value - random variable?

Question

Given that X,Y are RVs with an exponential distribution,
i.e. fx= e^(-x) and fy = e^(-y).
What is the mean of X*Y
The two functions are not independant and have limits from 0 to infinity.

correction:
fy= y*e^(-y)
and X and Y are related as follows:
Y= X+Z where fz=e^(-z)

Answer 1

You have said that they aren't independent; however, you have no mention of how they depend on each other. Therefore there is no way to calculate the answer.
If they *were* independent, then E[X*Y] = E[X]*E[Y]. Each one is an exponential distribution with lambda = 1, so the mean is just 1 (could also integrate e^(-x) from 0 to infinity, you also get 1.)

Answer 2

Random variable is 'quantity of extra team employed' enable x be the random variable28eb5ac48632646bba80ec2f19dd9860 It takes on 3 values one million(0.one million)+2(0.5)+5(0.4),one million(0.one million)+2(0.5)+5(0.4), and one million(0.one million)+2(0.5)+5(0.4) with possibilities zero28eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd9860, 28eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd9860 and nil28eb5ac48632646bba80ec2f19dd9860Four respectively28eb5ac48632646bba80ec2f19dd9860 X---P28eb5ac48632646bba80ec2f19dd9860X28eb5ac48632646bba80ec2f19dd9860 one million(0.one million)+2(0.5)+5(0.4)---zero28eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd9860 one million(0.one million)+2(0.5)+5(0.4)---zero28eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd9860 one million(0.one million)+2(0.5)+5(0.4)---28eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd9860Four E28eb5ac48632646bba80ec2f19dd9860x28eb5ac48632646bba80ec2f19dd9860 = [28eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd9860] = 28eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd9860Zero = 328eb5ac48632646bba80ec2f19dd986028eb5ac48632646bba80ec2f19dd9860