# Derive the expected value and variance of $Z$

Suppose $X$ is a random variable with mean $\mu$ and variance $\sigma^2.$ Let $$Z = \frac{X-\mu}{\sigma}.$$

Derive the expected value and variance of $Z$. Remember to justify all non-algebraic steps.

I thought that I could just plug in the value of $Z$ and find the expected value, but that's not it I don't think. This is just stumping me.

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