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= 1/26

Explanation:

The joint probability mass function for X and Y must comply that:

`\[\sum\]\sum\] c(x +y) = 1` for x∈{1,2,4} and y∈{1,3}

thus, all the possible values for the pairs (x,y) are:

(1,1) (1,3) (2,1) (2,3) (4,1) (4,3)

and then

c [(1+1)+(1+3)+(2+1)+(2+3)+(4+1)+(4+3)] = 1

c[26] = 1

c= 1/26