Question

Px(x) = The marginal pmf of each of X, Y variables is given below: 1 ; x = -1,3 4 y + 1 2 PY) = ; y = 1,2 - ; x = 1 5 4 0; Otherwise 0; Otherwise (a) If X, Y are independent random variables, then obtain and report the complete joint pmf of X, Y. Provide your answer in a tabular or functional form. (b) Compute the probability that sum of X and Y is less than 3. That is, find P(X+Y<3). (c) Compute the expected value of (X-Y)?/Y. Your final answer has to be a number.

Answer 1

Question (a - The joint pm.f. of X & Y is, prx, y) = P(x), ply) 1 2 x 2 X 1 3 20 - 14) (3) 1 (+)(3) (*)) (4)) öt ul- öl Nima mlo mi I 2)) 3 3 10 20 2 Answe (b) Plx+423) - Plx= -1,4=1) +P(x=-1, Y= 2)+ P(X=1,Y=1) 2+ 3+ 4 to + + 20 Answer 20 (0) E/(x-2)*) – ŽŽ x=> péry) كك x=-1 y=1

(10). PC, D + Ly: [1,2) + 4p (1) + G (2) + (3) + B) (2,2) = 4.() + () + O + 글(3) + 4 + 4 () + 글() + + 를 +3 + 27 40 164 27+6+ 1643 나이 89 [= 400 Auswa