# (1st Post) Estimating the transformation of a gamma random variable with a lognormal distribution

If X is gamma(n,$\lambda$) distributed, what should $\alpha$ and $\beta$ be such that the constructed random variable $\beta*exp(\alpha X)$ is approximated by the lognormal(0,1) distribution when n is sufficiently large. I have tried splitting the gamma variable into a sum of exponential variables and also tried Taylor expanding $\beta*exp(\alpha X)$ but neither seems to be working.

• What are your insights on the problem? Where exactly are you stuck? – Jan Feb 21 '17 at 0:00