Question

The random variables X and Y have the joint PMF
pX,Y(x,y)={c⋅(x+y)2,0,if x∈{1,2,4} and y∈{1,3},otherwise.
All answers in this problem should be numerical.

Find the value of the constant c.

c=

Answer 1

c= 5/64

P(Y<X)= 83/128

P(Y=X)= 1/32

P(X=1)= 10/64

P(X=2)= 17/64

P(X=3)= 0

P(X=4)= 37/64

E[X]= 3

E[XY]= 227/32

var(X)= 3/2

Answer 2

c=1/128