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that the new coordinate axes, while still being perpendicular, align well with sketched in part (a) below. (a) Sketch the area in the plane R? where fx.y is positive. (b) Do X, Y jointly follow a normal distribution? Justify your answer.

that the new coordinate axes, while still being perpendicular, align well with sketched in part (a) below. (a) Sketch the area in the plane R? where fx.y is positive. (b) Do X, Y jointly follow a normal distribution? Justify your answer.

MATLAB: An Introduction with Applications
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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part C and D

1. Let the joint pdf of X and Y be given by fx.y (r, y) Cexp 1 + ry y) 1(0,00) (x + y) where C > 0 is an unknown constant. Hint: this question encourages a geometric approach. In your integrations, you may wish to carry out a change of coordinates so that the new coordinate axes, while still being perpendicular, align well with the area sketched in part (a) below. (a) Sketch the area in the plane R? where fx,y is positive. (b) Do X, Y jointly follow a normal distribution? Justify your answer. (c) Decide whether g(x, y) = C' exp (-a2 + ry - u) defines a pdf on R2 (Note that g is only one factor of fxy, not the whole of fx.y). If yes, compute C". If no, show that there is no C" > 0 for which it is a pdf. Hint: Consider the change of coordinates w = x +y, z =x - y. (d) Compute the constant C.
Transcribed Image Text:1. Let the joint pdf of X and Y be given by fx.y (r, y) Cexp 1 + ry y) 1(0,00) (x + y) where C > 0 is an unknown constant. Hint: this question encourages a geometric approach. In your integrations, you may wish to carry out a change of coordinates so that the new coordinate axes, while still being perpendicular, align well with the area sketched in part (a) below. (a) Sketch the area in the plane R? where fx,y is positive. (b) Do X, Y jointly follow a normal distribution? Justify your answer. (c) Decide whether g(x, y) = C' exp (-a2 + ry - u) defines a pdf on R2 (Note that g is only one factor of fxy, not the whole of fx.y). If yes, compute C". If no, show that there is no C" > 0 for which it is a pdf. Hint: Consider the change of coordinates w = x +y, z =x - y. (d) Compute the constant C.
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