# Math Help - unbias estimates and variance?

1. ## unbias 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

2. can you work out $Var(\bar{x}) = Var \left( \frac{\sum x}{n} \right)$ ?

if so, you can use:
$Var(a \bar{x}) = a^2 var(\bar{x})$

which will give you $Var(\frac{\bar{x}}{2})$ and hence $Var(\hat{\mu_1})$

repeat the process to get $Var(\hat{\mu_2})$

Finally, you can use:
$Var(C + D) = Var(C) + Var(D) + 2Cov(C,D)$

to get the variance of the sum.

3. 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.

4. Originally Posted by SpringFan25
can you work out $Var(\bar{x}) = Var \left( \frac{\sum x}{n} \right)$ ?

if so, you can use:
$Var(a \bar{x}) = a^2 var(\bar{x})$

which will give you $Var(\frac{\bar{x}}{2})$ and hence $Var(\hat{\mu_1})$

repeat the process to get $Var(\hat{\mu_2})$

Finally, you can use:
$Var(C + D) = Var(C) + Var(D) + 2Cov(C,D)$

to get the variance of the sum.
$Var(a \bar{x}) = a^2 var(\bar{x})$
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 '',

5. Originally Posted by matheagle
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
yes so would i

but is not given

and yes the expected valuees are mu
as u obviously were able to figure this without me saying so my omision is justify

6. Originally Posted by Caption12
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
and who does moo hates? hates two? moo2hater? moohatter? madhatter?
I'm confused.