- #1
Hejdun
- 25
- 0
Hi everyone,
I have been struggling with an expectation for a while. It is seems very difficult (if not impossible) to find an analytical expression, but all hints and suggestions would be most appreciated. Here goes. I want to find an analytical expression (i.e. solve the integral) for the expectation
E[ X^2*exp(X)/(1+exp(X))^2 ], where X~N(0,σ^2)
That is, X is a r.v. that follows a normal distribution with mean 0 and variance sigma^2, and is then transformed according to the formula in the expectation above. Any hints or suggestions?
Best regards
Hejdun
I have been struggling with an expectation for a while. It is seems very difficult (if not impossible) to find an analytical expression, but all hints and suggestions would be most appreciated. Here goes. I want to find an analytical expression (i.e. solve the integral) for the expectation
E[ X^2*exp(X)/(1+exp(X))^2 ], where X~N(0,σ^2)
That is, X is a r.v. that follows a normal distribution with mean 0 and variance sigma^2, and is then transformed according to the formula in the expectation above. Any hints or suggestions?
Best regards
Hejdun