# Joint Probability Distribution

• November 25th 2009, 05:52 PM
Porter1
Joint Probability Distribution
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.
• November 25th 2009, 06:19 PM
matheagle
fill in that 2 by 2 table and calculate the means and variances
There are only 4 possibilities.
• November 25th 2009, 06:41 PM
Porter1
Im still a little confuse about using the equation to the table.
• November 25th 2009, 08:24 PM
matheagle
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 $P(Y_1=a,Y_2=b) = {a + 2b\over 18}$

NOW let (a,b) these four choices {(1,1),(1,2),(2,1),(2,2)}

Those four probabilities better sum to 1, otherwise..................