Question

4.2 The Correlation Coefficient 1. Let the random variables X and Y have the joint PMF of the form x + y , x= 1,2, y = 1,2,3. p(x,y) = 21 They satisfy 11 12 Mx = 16 of = 12 of = 212 2 My = 27 Find the covariance Cov(X,Y) and the correlation coefficient p. Are X and Y independent or dependent?

Answer 1

4/ 21 MI 72. +9773 Given pimf Pln, y) = nty n=112, 4x1,2,3 21 thon marginal pmf of v die Pax) IP193,4): į nty - 9:42. 4.mp3 P(x)= 3XL IPUM)= 3272 !?) marginal pmf of y I e Pio): E plin ) = 2 et 2 ItY2.ty 21 21 :P ) 3474,93143 from 0 to we can contude that . Play) # pec). PLY) henca xty are not independent Scanned with CamScanner .

NoD EX) > EB), - 대는 록을 써 시 EX)) 2. (x). - ite) + 50.0M)= = Ear-E097 : 14 | 72 1 19x721 1 그 - 1332 53-22 - 2 cs Scanned with CamScanner

329) = ㄷ 1 기 | 1 3376) 721 Now EX= [ 4. Ply) E ) | - (32) + 2 (32) + 3 (21) - + + 30te) 분을 CI P = 1 F (42)= [ 17. Poj 1 니 | 2 | | - 7. (324) + 2 (312 + (3123) 니 | 21 | 21 2 Now y) = y 2 Ely2) - (E tu?? '- 14 - (4) Scanned with CamScanner

11. HAWA? ='Hoofwel Pino Now I liv): < oyalty ny ?). N1 91 P [ *l (art) 4 . 2 (M2), :- [) 4 22 (nyt)30 (943) = 4 4 4 2 179)3-1143) 4 2014 2015) 43:2 27 (141) 2:11:)) 2) Ca Scanned with CamScanner

Now Con CX,Y) is defined as cou (x,y)= É %). -EQ). E(1) .-4.4 cov (X,Y) = 3.4285 - 1:5714 X2:1904 = 3:4285 = 3:44.21 I coulxi 4) 3. - 0.01361 Now correlatioon coethicient p is defined as ...cov til) -0.0136 P urxj. ve 22 - -0.0136 Jo. 2448 9 X 06303% P= -0.03461 Cs Scanned with CamScanner