fill in that 2 by 2 table and calculate the means and variances
There are only 4 possibilities.
Don't know what to do and need your help!
If Y1 and Y2 are random variables of the discrete type having the probability distribution
f(y1,y2) = (y1 + 2y2)/18, (y1,y2) = {(1,1),(1,2),(2,1),(2,2)}
(a) Find E(Y1 + 2Y2) and V(Y1 + 2Y2).
Hint: Make a joint probability distribution table.
E(Y1 + 2Y2) = E(Y1) + 2E(Y2) and V(Y1+2Y2) = V(Y1)+4V(Y2)+4Cov(Y1,Y2).
(b) Find the conditional mean and variance of Y2, given Y1 = 2.
I don't like these f's when dealing with discrete rvs
f(y1,y2) = (y1 + 2y2)/18, (y1,y2) = {(1,1),(1,2),(2,1),(2,2)}
should be
NOW let (a,b) these four choices {(1,1),(1,2),(2,1),(2,2)}
Those four probabilities better sum to 1, otherwise..................