1. random variable

Let $\displaystyle \mu$ and $\displaystyle \sigma^{2}$ denote the mean and variance of the random variable X. Determine $\displaystyle E[\frac{(X-\mu)}{\sigma}]$ and $\displaystyle E{[\frac{(X-\mu)}{\sigma}]^{2}}.$Thank you for your help.

2. Hello,
Originally Posted by laser
Let $\displaystyle \mu$ and $\displaystyle \sigma^{2}$ denote the mean and variance of the random variable X. Determine $\displaystyle E[\frac{(X-\mu)}{\sigma}]$ and $\displaystyle E{[\frac{(X-\mu)}{\sigma}]^{2}}.$Thank you for your help.
Remember this : $\displaystyle \mathbb{E}(aX+b)=a\mathbb{E}(X)+b$

For the second one, by seeing your latex code, I guess you actually meant :
$\displaystyle \mathbb{E}\left(\left[\frac{(X-\mu)}{\sigma}\right]^2\right)$

Note that, by definition of the variance, it equals $\displaystyle \text{Var}\left(\frac{(X-\mu)}{\sigma}\right)+\left(\mathbb{E}\left(\frac{( X-\mu)}{\sigma}\right)\right)^2$

And remember that $\displaystyle \text{Var}(aX+b)=a^2 \text{Var}(X)$

You should know have all the necessary stuff for answering your questions