Joint PMF: Value of c, P[Y<X], P[Y>X], P[Y=X], P[X<1]

[hxluo]

Random variables X and Y have the joint PMF

PX,Y(x,y) = c|x+y| x=-2,0,2; y=-1,0,1. 0 otherwise

1) what is the value of constant c?
2)what is P[Y<X]?
3)What is P[Y>X]?
4)what is P[Y=X]?
5)what is P[X<1]?

 

[happyg1]

What did you try?
For a Probability Mass Function to BE a PMF, the sum over the ENTIRE space HAS to be 1...
What can you do to solve the first problem about C?...You have to sum it up ALL TOGETHER and set it to 1. (you might like to set it up in table form)...then,
Solve for C...the rest will fall out of that.
CC