# What is the formula for the Mean & Variance for this Log Normally Distributed Variable

I am having trouble finding the mean and variance for this log normal distribution.

• Wikipedia gives expressions for the mean and variance of a log-normal distribution, i.e. for $\frac{c_{t+1}}{c_t}$ Sep 25 at 15:11
• if $X$ is lognormal $E(X^t)$ is not hard to do by evaluating the integral (you can get what you want from $t=1,2$), but easier still is to obtain it directly from the MGF of $\log(X)$ (a normal distribution), assuming you've already done (or otherwise have) that calculation. I believe some answers on site already have the result. Sep 25 at 15:40