1. ## need help pmf

1. The joint probability distribution of two discrete random variables X and Y are given by the following joint probability mass function:

P( X=x, Y=y ) = k | x – y |, x = 1, 2, 3 ; y = 2, 4, 5
= 0, otherwise.

(a) Find the constant k
(b) Find the marginal distributions of X and Y
(c) Calculate the correlation coefficient between X and Y
(d) Are X and Y Independent ?

2. Originally Posted by amul28
1. The joint probability distribution of two discrete random variables X and Y are given by the following joint probability mass function:
P( X=x, Y=y ) = k | x – y |, x = 1, 2, 3 ; y = 2, 4, 5
= 0, otherwise.
(a) Find the constant k
Let $\displaystyle A = \left\{ {1,2,3} \right\} \times \left\{ {2,4,5} \right\}~$then $\displaystyle ~k = \left( {\sum\limits_{(x,y) \in A} {\left| {x - y} \right|} } \right)^{ - 1}$.

3. so is it equal to 1/6 ?

4. Originally Posted by amul28
so is it equal to 1/6 ?
There are nine pairs in $\displaystyle A$.
You have to sum nine numbers to get $\displaystyle k$.

5. Originally Posted by Plato
There are nine pairs in $\displaystyle A$.
You have to sum nine numbers to get $\displaystyle k$.

so it is 1/17

6. Originally Posted by amul28
so it is 1/17
Yes it is.