- #1
sara_87
- 763
- 0
Homework Statement
X1 and X2 are independent random variables. They both have the same mean (mue). Their variances are s1^2 and s2^2 respectively, where s1^2 and s2^2 are known constants. It is proposed to estimate mue by an estimator T of the form T=c1X1 + c2X2.
Show that T will be unbiased if c1 + c2=1
and find an expression for var(T) in terms of c1, s1^2 and s2^2.
(assuming c1+c2=1)
Homework Equations
The Attempt at a Solution
I showed that T will be unbiased if c1+c2=1
For the next part this is what i did:
var(T) = var(c1X1+c2X2)
var(c1X1+c2X2) = E[(c1X1+c2X2)^2] + {E[c1X1+c2X2]}^2
and then after expanding and simplifying, i got:
var(T) = 2(mue)^2(c1^2 + 2c1c2 + c2^2)
I can easily change c2 in terms of c1 but how do put in terms of s1^2 and s2^2 as this is what they are asking for??
Thank you