Bias and Variance of Estimators for Population Mean

[gutnedawg]

Homework Statement

Suppose you have a random sample {X1,X2,X3} of size n=3. Denote the population mean \mu = E(Xi) and the population variance \sigma^2= VAR(Xi). Consider the following three estimators for \mu

\mu 1= X
\mu 2= X1/5 +X2/2 +X3/5
\mu 3= (X1+X2+X3)/5

What is the bias associated with each estimator?
What is the variance associated with each estimator?

Homework Equations

I'm not sure

The Attempt at a Solution

I'm really at a loss now.

 

[xxxx]

hey guys,how do i post my questions

 

[statdad]

Homework Statement

Suppose you have a random sample {X1,X2,X3} of size n=3. Denote the population mean \mu = E(Xi) and the population variance \sigma^2= VAR(Xi). Consider the following three estimators for \mu

\mu 1= X
\mu 2= X1/5 +X2/2 +X3/5
\mu 3= (X1+X2+X3)/5

What is the bias associated with each estimator?
What is the variance associated with each estimator?

Homework Equations

I'm not sure

The Attempt at a Solution

I'm really at a loss now.

For each estimator use the rules for expectations and variances of linear combinations of independent variables.

<br /> \begin{align*}<br /> E(aX + bY) &amp;= aE(X) + bE(Y) \\<br /> Var(aX + bY) &amp; = a^2 Var(X) + b^2 Var(Y)<br /> \end{align*}<br />

Try these with your estimators and show what you find.