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Expectation of (non-linear) transformed random variables

Mathematics Asked by Selos on December 27, 2021

If I have a two correlated normal distributed random variables, i.e. $A sim N(m_a,sigma_a^2)$ and $B sim N(0,1)$, with correlation coefficient $ Corr(A,B) =rho$, then I want to define a random variable $ R = e^{frac{1}{2}A}B$.

I found out that $ E[R] = frac{1}{2} rho sigma_a^2 e^{frac{1}{2}m_a + frac{1}{8}sigma_a^2}$

My question: What ist $E[R^2]$ ?

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