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QUESTION 12 Let Y1 and Y2 be continuous random variables with the joint p.d.f. (probability density function) f(V1, V2) given by 23 v 2² v2 V1 V2 for -2 S Vis 1 and 0 Sy2 si fly1, y2) = 0 elsewhere Find the joint c.d.f. (cumulative distribution function) of the bivariate random variables Y1 and Y2 os 2 0 2 3 1 2 ² 1 2 o (v?? + 8) vz?

Answer 1

Question 12 Here Yi & Yz be contineous 8.1 with joint pdf 2 FC42Y2) = 2 4 ² Y2 -269, 41 of OS yes! j elsewhere Now joint codif of Yo & Y2 У! Ҷо = (رلارلا )F f ff Vos V2) dvi dve O -2 Y, 92 2 3 2 vo dv dva -2 yi 2 Y2 F v, 3 dvi 2 0 -2 yl 2 = 2 3 f 12 o) dvi -2 오 प्र 2 y ² - v² dvi 6 2 24,2 1,3 [ 13 Y, 6 -2

.: FC YoY2) = 242 8 [ y3 3 + 6 3 2 Y2 3+8) g = (دلاورلا) . . g (9, d y cy8+8) Hence joint codif of Yle X2 is & (y3+8) y? 3 last option correct.

QUESTION 12 Let Y1 and Y2 be continuous random variables with the joint p.d.f. (probability density function) f(V1, V2) given by 2 - vz? rz Vi? V2 for – 2 svi s 1 and 0 Sy2 31 f(V1, V2) = 3 O elsewhere Find the joint c.d.f. (cumulative distribution function) of the bivariate random variables Y1 and Y2 9 V1² r2² Y1ºY2 (Vi} + 8) vz? 9