Expected value of squared sample mean

[safina]

May I ask how come that E[$$\bar{X}^{2}$$] = $$\frac{\sigma^{2}}{n}$$ + $$\mu^{2}$$?

 

[statdad]

Remember that for any random variable $Y$

$$E[Y^2] = Var(Y) + \mu_Y^2$$

What do you know about the mean and variance of the sample mean?

 

[safina]

Remember that for any random variable $Y$

$$E[Y^2] = Var(Y) + \mu_Y^2$$

What do you know about the mean and variance of the sample mean?

Okey, the mean of the sample mean is mu and the variance of the sample mean is sigma squared divided by n.

Thsnk you!