Joint distribution

Question

The random variable X and Y have joint distribution

P(X=i, Y=j) =c(i+j), for i =0,1 ; j=1,2,3.

(i) 1/6

(ii) 1/9

(iii) 1/12

(iv) 1/15

Answer 1

The question is incomplete here but it appears the intended question is to find the value of c, given the above formula defines a joint distribution. In this case, it would help to make a table of values of P(X = i, Y = j). The sum of the values must be 1, i.e., c + 2c + 2c + 3c + 3c + 4c = 1. Thus 15c = 1, or c = 1/15 -- (iv).