Question

0 3-) Common probability function of x andy; flory) qalxo), AE {1982, y equili?? day al find the constant "C". bl find the marginal probability fuctions of x ad y c) Are X and Y independent a d) Plx<2) ,P ( X 7 Y) ,P(x+482) and Plx 22 (441) fud the probability.

Answer 1

Jiren Joint to trud Such that fx,y (2, 4) = calaty) + XE {1, 2, 3} ye{o, 1, 2} table continguny put us for Joint X 1 z 3 fyly) с o 27 8C 140 } 6c 221 20C 2 36 с. ISC 26C Sy(2) 79 281 36C Legitimate praf I fx, 4(1,9) = 1 _25 709 C 1 60 ca 6o

Marginal -pruf of x. - X xx) 2 6 3 16 60 36 60 Marginal tho trud Q 1 2 14 fyly) 14 po 26/60 for XU 4 To (2,4). be independent fx (n) f(y) tasy ow 1) X! 7 y=0 fx 0, 1) = 6 60 & fx!!) & fylol = 14 70 60 11 yly) 6 X4 3600 0.023 33 . 0.01666 Z $x,y1,0): 08② => 60 T fxyglu, y) # fxla) fyly) hot independent

in p[x2] p[x=1] 10 1) P[x4] + fasth 10) #4,12,47 P x=y] +P [x>y] #x2442, 1) + 1444(22) + fx, 4(2, 1) + fx7(3,0) + fx, 4(3,1) fx1413, 2) OR OR OR 1. P[x4] [ fxg4442)] OR P[X7,4] 3 60 0.95 ii) P L X+Y42] P [x = , 4:01 FP[x = 2,4+0] + P[X=1,4=1} 20 + 60 4 60 + 2 GO 7 60 n ivy PL 83,2 145 1] PLx72 8451 P[ysi Now PLx7,2 & Yel P[x = 2, y=0] + P{ x=2 , 9 = 1 P[*23, =0 ] + P[x = 3, 457 AF BOL + g 60 6 60 + L 60

34 3L शिकx 34 60 31 15 2 x To 60 ५६ (1)F (0) 31 [15] ग 8 3L [156 24x)