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

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

what is

i) $\displaystyle

E(X_i \bar{X}), where \bar{X}= (\sum{X_i})/n

$

ii) $\displaystyle

E(\bar{X}^2)

$

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

thanks a lot