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=
Find P(Y<X).

P(Y<X)=
Find P(Y=X).

P(Y=X)=
Find the following probabilities.

P(X=1)=
P(X=2)=
P(X=3)=
P(X=4)=
Find the expectations E[X] and E[XY].

E[X]=
E[XY]=
Find the variance of X.

var(X)=

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

Wrong answer for c

Answer 3

c=1/128