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Stat 515 Final Exam Practice Problems + Solution

Prof. H. K. HsiehStat 515 Final Exam Practice Problems + SolutionStudent s Name:Section:.NOTE: Write main steps of your work clearly and circle your Suppose that the joint ofXandYis given byf(x,y) = 8xy,0<x<y<1= 0elsewhere(a) Verify that thef(x,y) given above is indeed a : 10 y08xydxdy= 104yx2]y0dy= 104[y3]dy=y4]10= ,f(x,y) is a pdf.(b) Find the marginal probability density ofX,f1(x).Answer:f1(x) = 1x8xydy= 4xy2]1x= 4x(1 x2),0<x<1.(c) Find the marginal probability density ofY,f2(y).Answer:f2(y) = y08xydy= 4yx2]y0= 4y3,0<y<1.

Stat 515 Final Exam Practice Problems + Solution Student’s Name: Section: . NOTE: Write main steps of your work clearly and circle your answers. 1. Suppose that the joint p.d.f. of X and Y is given by f(x,y) = 8xy, 0 < x < y < 1 = 0 elsewhere (a) Verify that the f(x,y) given above is indeed a p.d.f. Answer: Z 1 0 Z y 0 8xydxdy = Z 1 0 4yx2]y ...

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