/ Suppose that three random variables X1, X2, and X3 have a continuous joint distribution for which the joint p.d.f. is as follows: 8x1x2x3 for 0 < x; < 1 (i = 1, 2, 3), f (x1, x2, x3) = 0. { otherwise. Suppose also that Y1 = X1, Y2 = X1X2, and Y3 = X1X2X3. ind the joint p.d.f. of Y1, Y2, and Y3. %3D

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 43CR
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Suppose that three random variables X1, X2, and Xa
have a continuous joint distribution for which the joint
p.d.f. is as follows:
= ! S*;*2*3_for 0 < x; < 1 (i = 1, 2. 3),.
otherwise.
8x1x2x3 for 0 < x; < 1 (i = 1, 2, 3),
f (x1, x2, X3)
|3|
0.
Suppose also that Y1 = X1, Y2 = X1X2, and Y3= X1X2X3.
Find the joint p.d.f. of Y1, Y2, and Y3.
%3D
%3D
%3D
Transcribed Image Text:Suppose that three random variables X1, X2, and Xa have a continuous joint distribution for which the joint p.d.f. is as follows: = ! S*;*2*3_for 0 < x; < 1 (i = 1, 2. 3),. otherwise. 8x1x2x3 for 0 < x; < 1 (i = 1, 2, 3), f (x1, x2, X3) |3| 0. Suppose also that Y1 = X1, Y2 = X1X2, and Y3= X1X2X3. Find the joint p.d.f. of Y1, Y2, and Y3. %3D %3D %3D
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