rp2000ap
Mar22-09, 08:59 PM
1. The problem statement, all variables and given/known data
Let Z be a standard normal random variable, f is a measurable function and a is a constant.
Show E[Zf(e^aZ)] = aE[e^aZ]E[f'(e^(a(Z+a))]
2. Relevant equations
3. The attempt at a solution
I set up an integral from negative to positive infinity of
z*f(e^aZ)*e^((-z^2)/2)*1/sqrt(2pie)*dz
My 2 questions are can I combine the z from the pdf of the normal distrbution function into f(e^aZ) and does the z in the beginning of my equation require integration by parts to evaluation the integral.
Thanks!
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
Let Z be a standard normal random variable, f is a measurable function and a is a constant.
Show E[Zf(e^aZ)] = aE[e^aZ]E[f'(e^(a(Z+a))]
2. Relevant equations
3. The attempt at a solution
I set up an integral from negative to positive infinity of
z*f(e^aZ)*e^((-z^2)/2)*1/sqrt(2pie)*dz
My 2 questions are can I combine the z from the pdf of the normal distrbution function into f(e^aZ) and does the z in the beginning of my equation require integration by parts to evaluation the integral.
Thanks!
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution