# Math Help - Expected Value

1. ## Expected Value

For a sample of identically and independently distributed variables , each having a mean μ and variance $\sigma^2$

for $\subscript{i}=1, 2, ...., n$

what is
i) $
E(X_i \bar{X}), where \bar{X}= (\sum{X_i})/n
$

ii) $
E(\bar{X}^2)
$

iii) $E[\bar{X}(X_i-\bar{X})]$

thanks a lot

2. Originally Posted by cky78
For a sample of identically and independently distributed variables , each having a mean μ and variance $\sigma^2$

for $\subscript{i}=1, 2, ...., n$

what is
i) $
E(X_i \bar{X}), where \bar{X}= (\sum{X_i})/n
$

ii) $
E(\bar{X}^2)
$

iii) $E[\bar{X}(X_i-\bar{X})]$

thanks a lot
Because $X_i, \ X_j , \ i\ne j$ are independent $E(X_iX_j)=\mu^2$ (just write out the expectation of the product and observe that independence means that $p(x_i,x_j)=p(x_i)p(x_j)$)

Then the rest should follow easily

(you might also need $E(X_iX_i)=\sigma^2+\mu^2$ )

CB