unbias estimates and variance?

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April 7th 2011, 02:09 AM
Caption12

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
April 7th 2011, 10:05 AM
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.
April 7th 2011, 11:38 PM
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

AND I guess, both the expected value of the X and Y is this mythical Moo.
April 9th 2011, 12:19 PM
Caption12

Quote:

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 '',
April 9th 2011, 12:44 PM
Caption12

Quote:

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 ;)
April 9th 2011, 03:18 PM
matheagle

Quote:

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.