# i.i.d random variables

• Oct 2nd 2009, 04:33 AM
sirellwood
i.i.d random variables
Suppose W, X, Y and Z are i.i.d random variables with mean "mu" = -9 and standard deviation "sigma" = 6

Find the expectation and variance of each of the following estimators of "mu"

1. A = 8W + 3X - 4Y - 6Z

i got E(A) = -9 and Var(A) as 3976.... however i am having problems knowing whether i was right to convert the SD of 6 to a variance of 36?

2. B = 1/28(8W + 6X +2Y +9Z)

3. C = 33W + 4Y - 36Z

Which estimators are unbiased for "mu"?

Which estimator is the most efficient?

Find E(YW)
• Oct 4th 2009, 04:48 AM
mr fantastic
Quote:

Originally Posted by sirellwood
Suppose W, X, Y and Z are i.i.d random variables with mean "mu" = -9 and standard deviation "sigma" = 6

Find the expectation and variance of each of the following estimators of "mu"

1. A = 8W + 3X - 4Y - 6Z

i got E(A) = -9 and Var(A) as 3976.... however i am having problems knowing whether i was right to convert the SD of 6 to a variance of 36? Mr F says: You were right. Do the others the same way.

2. B = 1/28(8W + 6X +2Y +9Z)

3. C = 33W + 4Y - 36Z

Which estimators are unbiased for "mu"? Mr F says: Which estimators have an expected value equal to mu ....?

Which estimator is the most efficient? Mr F says: What does the definition of efficient tell you ....?

Find E(YW)

$\displaystyle E(YW) = \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} yw f(y, w) \, dw \, dy$ where $\displaystyle f(y, w) = f(y) f(w)$ is the joint pdf of Y and W ....