# Thread: Joint Probability mass problem

1. ## Joint Probability mass problem

Hello All,

This is my first time visitnig math helop forum and I was wondering if anyone could help me with a HW problem. I have posted it below. Thanks a lot:

1. The problem statement, all variables and given/known data

X and Y are random variables and have the following joint probability mass function

q(x,y)=1/p^2 for x=1,2,....p and y=1,2,....p

are x and y independent?

2. The attempt at a solution

What I want to do is find the marginals for x and y and then see if q(1,1) is equivalent to qx(1) times qy(1)

I know the marginal for x is the summation from y=1 to p of 1/p^2. Y is the same except switch to x for the summation. I just don't know how to get the summation. Can anyone help with this?

Secondly, can P(1,2) even exists? Don't the x and y values have to be the same since p(x,y) is 1/p^2 and if x and y are different, what value would you use for p?

I'm completely lost and I would appreciate all help. Thanks.
I would appreciate any help with this problem. Thank You.

2. Originally Posted by jackroberts4
Hello All,

This is my first time visitnig math helop forum and I was wondering if anyone could help me with a HW problem. I have posted it below. Thanks a lot:

1. The problem statement, all variables and given/known data

X and Y are random variables and have the following joint probability mass function

q(x,y)=1/p^2 for x=1,2,....p and y=1,2,....p

are x and y independent?

2. The attempt at a solution

What I want to do is find the marginals for x and y and then see if q(1,1) is equivalent to qx(1) times qy(1)

I know the marginal for x is the summation from y=1 to p of 1/p^2. Y is the same except switch to x for the summation. I just don't know how to get the summation. Can anyone help with this?

Secondly, can P(1,2) even exists? Don't the x and y values have to be the same since p(x,y) is 1/p^2 and if x and y are different, what value would you use for p?

I'm completely lost and I would appreciate all help. Thanks.
I would appreciate any help with this problem. Thank You.
The marginal distribution of $x$ is:

$\displaystyle P_X(x)=\sum_{i=1}^p \frac{1}{p^2}=\frac{1}{p},\ \ x=1,..,p$

similarly the marginal distribution of y is:

$\displaystyle P_Y(y)=\sum_{i=1}^p \frac{1}{p^2}=\frac{1}{p},\ \ y=1,..,p$

We now observe that:

$q(x,y)=P_X(x)P_Y(y)$

and so $X$ and $Y$ are independent.

CB