Question

Let (X,Y) have joint pdf given by I c, \y < x, 0 < x < 1, f(x, y) = { | 0, 0.W., (a) Find the constant c. (b) Find fx(r) and fy(y) (c) For 0 < x < 1, find fy\X=z(y) and HY|X=r and oſ X=z- (d) Find Cov(X, Y). (e) Are X and Y independent? Explain why.

Answer 1

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Eyh)Syfyndy ५ % - - ৫ J9 4५ ৬2, L -)=০ 2x 2 4X0 = v(\2= Eশ) - y+) ECY212 - ০ कृटि) वप जं + ५= त्र श् (4) cov Cx2= £xY2-৪£५ र्गु स्मित सु शषुर्वकपुवंणुबे० युर वचु कर = ০ ५-* স । (५) -10x (५५-) 2. 1০

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