need help for calculating an expectation

Huanghanming · September 22nd, 2010, 4:48 am

can anyone help me for calculating this expectation? Thanks a lot!where are correlated normal random variables with coefficient c.

DevonFangs · September 22nd, 2010, 5:40 am

It's not so hard.You know the pdf of two correlated r.v., what can you do then?

Antonio · September 22nd, 2010, 6:10 am

http://en.wikipedia.org/wiki/Multivaria ... stribution

Huanghanming · September 22nd, 2010, 6:26 am

I have got it. thanks.

Huanghanming · September 22nd, 2010, 6:29 am

QuoteOriginally posted by: DevonFangsIt's not so hard.You know the pdf of two correlated r.v., what can you do then?but how to calculate the covariance of the lognormal and the normal r.v. ?

DevonFangs · September 22nd, 2010, 7:57 am

Just write down the integral as the very definition of expected value

rg209 · September 22nd, 2010, 9:02 pm

How about conditioning wrt to x_1.E(x_1 * exp(x_1+x_2)) = E( x_1* exp x_1 E( exp x_2 / x_1))

Huanghanming · September 23rd, 2010, 6:37 am

you are right. just some tedious calculation... ~>_<~QuoteOriginally posted by: DevonFangsJust write down the integral as the very definition of expected value

Huanghanming · September 23rd, 2010, 6:44 am

the calculation for the conditional expectation is the same tedious as directly applying the bivariate normal density....QuoteOriginally posted by: rg209How about conditioning wrt to x_1.E(x_1 * exp(x_1+x_2)) = E( x_1* exp x_1 E( exp x_2 / x_1))