Let X1 and X2 be independent N (0, 1) and x(r), respectively. Consider the following transformation X1 andY2 = X2 %3D %3D VX2/r • [[a)] Find the Jacobian of this transformation. • [(b)] Find the joint distribution of (Y1, Y2)'. • [[c)] Find the two marginal pdfs of Y1 and Y2.

Let X1 and X2 be independent N (0, 1) and x(r), respectively. Consider the following transformation X1 andY2 = X2 %3D %3D VX2/r • [[a)] Find the Jacobian of this transformation. • [(b)] Find the joint distribution of (Y1, Y2)'. • [[c)] Find the two marginal pdfs of Y1 and Y2.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Let X1 and X2 be independent N(0, 1) and x(r), respectively. Consider the
following transformation
Y1 =
X1
andY2 = X2
%3D
VX2/r
• [(a)] Find the Jacobian of this transformation.
• [(b)] Find the joint distribution of (Y1, Y2).
[(c)] Find the two marginal pdfs of Y and Y2.
• [(d)] Are Y1 and Y2 independent? Justify your answer.

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