How do you derive Mean and Variance of Log-Normal Distribution?
I found out the probability function
But I don't know how to derive E(X) and Var(X) without using integration.
Thank you, 892king
Use momentgenerating function
Actually using the moment generating fuction is quite easy to derive the moments of the lognormal:
E(exp(t*log(X)) = E(X^t)...(1)
also because log(X) is normal:
E(exp(t*log(X)) = exp(ut+st^2/2)...(2)
Then from (1) and (2) substituting with t = n:
E(X^n) = exp(un+sn^2/2)
From here you can easily obtain the mean and the variance.