# Thread: Joint Distributions and a 3rd Variable

1. ## Joint Distributions and a 3rd Variable

I am struggling with this probability problem.

Consider the random variables X and Y with joint distribution as given below.
X
0 1
Y 1 .2 .2
2 .5 .1
1

Calculate the probability mass function of the new random variable Z≡X+Y

z___|____|____|______|_____|
p(z)_|____|____|______|_____|

Calculate the variance of Z, V[Z]≡σ_Z^2 and show that V[Z]=V[X]+V[Y]+2cov[X,Y].

I am not sure how to complete the table. I think that I may be able to work on the variances on my own.

2. ## Re: Joint Distributions and a 3rd Variable

So in the given joint pmf table, you see there is 4 support points (possible cases) for . Try to see what value does take in each case and you fill the table accordingly. As you may expected, sometimes you may have two or more different cases having the identical value of , which you will need to sum the probabilities of those cases for the pmf of .

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