consider the unbias estimaters mu1hat = 1/2 xbar + 1/2 ybar. and mu2hates = 1/3 xbar + 2/3 ybar. calculate the variance of mu1hat and mu2hats
can you work out $\displaystyle Var(\bar{x}) = Var \left( \frac{\sum x}{n} \right)$ ?
if so, you can use:
$\displaystyle Var(a \bar{x}) = a^2 var(\bar{x}) $
which will give you $\displaystyle Var(\frac{\bar{x}}{2})$ and hence $\displaystyle Var(\hat{\mu_1})$
repeat the process to get $\displaystyle Var(\hat{\mu_2})$
Finally, you can use:
$\displaystyle Var(C + D) = Var(C) + Var(D) + 2Cov(C,D)$
to get the variance of the sum.
$\displaystyle Var(a \bar{x}) = a^2 var(\bar{x}) $
i have never herd this one it is nt in my sylabus
covarance is also not in my sylabus and i dont know any resource i cn find to find this one out.. i looked on many website and i not find ...
also there is not muhat 1 and muhat 2. .. it is muonehat and mutwo hats. like U '',