$X$ is a random variable for normal distribution: $X\sim N(\mu, \sigma^2)$.
What is the mean and variance of $\exp\{x\}$?
My attempt:
$$E[\exp\{x\}]=\exp \{E[x]\} \text{, by the invariance property?}$$
$$\operatorname{var}(\exp\{x\})=\exp\{\operatorname{var}(x)\}, \text{ similarly}$$
This looks too easy, probably not right.
Should I look at exp{x} as a whole. use moment generating function?
But normal pdf requires $\exp\{x^2\}$. I'm stuck.