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)=
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
Wrong answer for c
c=1/128
c= 1/63
P(Y<X)= 7/9
P(Y=X)= 2/9
P(X=1)= 1/9
P(X=2)= 2/9
P(X=3)= 0
P(X=4)= 2/9
E[X]= 35/9
E[XY]= 110/21
var(X)= 5.729