Observations Y1, ,Yn are made according to the model Yi xi i, where x1, ,xn are fixed constants and 1, ,n are iid n(0, 2) Let and denote MLEs of and (a) Assume that x1, ,xn are observed values of iid random variables X1, ,Xn with distribution n(X, 2X) Prove that when we take expectations over the j...

a E E EE E E E EE E b Recall VarY ...

Observations Y1,... ,Yn are made according to the model Yi = + xi + i, where

Question:

Observations Y1,... ,Yn are made according to the model Yi = α + βxi + εi, where x1,...,xn are fixed constants and ε1,...,εn are iid n(0, σ2). Let and denote MLEs of α and β.
(a) Assume that x1,...,xn are observed values of iid random variables X1,...,Xn with n(μX, σ2X). Prove that when we take expectations over the joint of X and Y, we still get E = α and E = = β.
(b) The phenomenon of part (a) does not carry over to the covariance. Calculate the unconditional covariance of and (using the joint of X and Y).
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...