Covariance between lognormal and normal random variable

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Good evening,

I have the following question: Lets assume X is normally distribued and Y is log normal. Now, i want to obtain the covariance between both random variables. I am aware that: Cov(X,Y) = E(XY) - E(X)*E(Y)

While E(X) and E(Y) are easy to obtain, can somebody give me a (closed form) solution for E(XY)?

Best, Thomas