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

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- Apr 7th 2011, 01:09 AMCaption12unbias estimates and variance?
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

- Apr 7th 2011, 09:05 AMSpringFan25
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. - Apr 7th 2011, 10:38 PMmatheagle
I would like to know a lot more information,

such as the sample sizes, the covariance between the X's and Y's

the variance of X and also of Y

AND I guess, both the expected value of the X and Y is this mythical Moo. - Apr 9th 2011, 11:19 AMCaption12
$\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 '', - Apr 9th 2011, 11:44 AMCaption12
- Apr 9th 2011, 02:18 PMmatheagle