Let y be a random variable with E(y) = and Var(y) = 2. Show that E y = 0 and Var

Let y be a random variable with E(y) =μ and Var(y) =σ 2. Show that E



y−μ

σ



= 0 and Var



y−μ

σ



= 1.

Let ¯ y· be the sample mean of n independent observations yi with E(yi) = μ and Var(yi) =σ 2.

What is the expected value and variance of

¯ y·−μ

σ /

√

n

?

Hint: For the first part, write y−μ

σ

as 1

σ

y− μ

σ

and use Proposition 1.2.11.