Question

0<x<2, 0<y<1 23. The joint pdf of X and Y is fx.y(x, y)= (region below). 3 0 otherwise a) Determine f(y) b) Determine fx, (x) c) Determine E[Yx] d) Determine E[X|y] 0 1 2 24. Suppose that the joint probability density function of the jointly continuous random variables X and Y is x on the given region fxy(x,y)= 11 10 otherwise Determine fyly) 1 _$6x 0<x< y1 25. Let X and Y be continuous random variables with joint pdf fx. (x, y) = 70 otherwise 2 Given that E[x] = 3 and E[Y] =_, determine Cov[X,Y]. 0sysxs1 Determine E[Yx] 26. Given fxy(x, y)= 12' 10 otherwise 16x 0<x<y<1 27. Given fxy(x,y)= 10 otherwise and that E[X]= a determine Cov[X,Y] 28. Let X and Y be continuous random variables with joint pdf fxy(x, y) = { (v) 6x 0<x<y<1 10 otherwise Given that E[x] = and E[Y] = , determine Cov[X,Y). 29. Given that V[x]= 1.2, V[Y]=.8 and Cov[X,Y)=-4 determine V [3X – 5Y] 30. Given that V[x] = 2.1, V [Y]=1.5 and Cov[X,Y)=-4 determine V (2x – 4y] 31. Given that V[x]= 2.1, V[Y]=1.5 and Cov[X,Y]=5 determine V (2x +4Y]

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Answer 1

eThe maginal Ht of x (2x+1) The Conditienl pdf of y sven x fons) :0MC2, ocyc/ 2 CH4) ty (9/) żc2 )Th marginadf of y ( + 23) - (+1) 7he Carnditional of x gven Y ocr2,0Cy2 |1স৬) 17 ECI) 2 aHH) 17 (2xtl) 2 () 7 ocxe2 () )E(XI)= 3 20148): 1 (4+2) 2(1+9) 2CH) (3+y) 1+Y yel