Question

(8pts) 1. The joint probability density of X and Y is given by + 0<x<1 and 0 <y< 2 otherwise a) Verify that this is a joint probability density function. b) Find P(x >Y). o) Find Pſy > for<

Answer 1

OLALI f(x,y)5 (+12) OLJL2 o w Stray) da dy = 1 s (as da da af xy ) dady [ 6+ z.) dy 5x2 a this is joind pdf..

( X7Y 6 (2²pa) da dy 9 $ 34-6133 + da HUEBE. f (a) = S Flaing dy amt da

172% dada x</ © 2 ( ktore (hetk) ( ) - fix) [ + : up (te tyr) ;; Croy

+ ****yakan - (-) 1-03-) *4 + (-u) 15 8x2 8X4 6 4X4 256 -- 0.5625 to.4687 -0.058 = 0.9726 3 @ Elxy) = SS xy S (224 24 ) dx dy = 6 xey + xy dx dy

1 1 ), + (2) 4 - 9f8 Ex) x.fcx).dx ,x.fexo.dx 을 (2y4xd 돌부종

FOLLLL A 7 E (x²)= 65 x² (2x² + x) dx - 14 ) 0 CCOCES 3424 아21 - ops E} - [Ex))? N) - koo 50hO= 외 를 어 11 (2) 음 록t 운 t 57 Esott soos

6699 (4 + 2, 1) da 7X3 - 0.76+ 0.859) -1.6171 2 Vly) = Ely?) -(E(N)] ? 1,6171- (.14)? z 03175 Cov(x, y) = E(XY) - E(X). Ely) = 0.8ogs-0.7181.14 @ 0.000123 @ Sri cov (ory) 0.000123 (x). VCM √ 0.3175Koosig ooooks 0.128.3 0.0009584
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