Let X and Y be independent normally distributed random variables with ean zero and variances of = 1 and of = 4. (a) Write the joint probability density function fx.y(r, y). (b) Define new random variables U = aX +Y and V = X- Y, where a + -1 is a real number. Find the absolute value of the Jacobian of transform from X,Y to U, V. (c) Find the joint probability density function for U and V. Find a for which U and V are independent random variables. Write down fu.v (u, v) for this a in the answer.
Let X and Y be independent normally distributed random variables with ean zero and variances of = 1 and of = 4. (a) Write the joint probability density function fx.y(r, y). (b) Define new random variables U = aX +Y and V = X- Y, where a + -1 is a real number. Find the absolute value of the Jacobian of transform from X,Y to U, V. (c) Find the joint probability density function for U and V. Find a for which U and V are independent random variables. Write down fu.v (u, v) for this a in the answer.
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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![Let X and Y be independent normally distributed random variables with
mean zero and variances og = 1 and of = 4.
(a) Write the joint probability density function fx.y (r, y).
• (b) Define new random variables U = aX + Y and V = X – Y, where
a + -1 is a real number. Find the absolute value of the Jacobian of
transform from X, Y to U, V.
(c) Find the joint probability density function for U and V. Find a for
which U and V are independent random variables. Write down fu,v (u, v)
for this a in the answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe13a3d4-ca9f-45e2-9682-6f988ba982cc%2F74222a4f-42a9-4c2f-9e17-ddd07a93f3b2%2Fp7lgbh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let X and Y be independent normally distributed random variables with
mean zero and variances og = 1 and of = 4.
(a) Write the joint probability density function fx.y (r, y).
• (b) Define new random variables U = aX + Y and V = X – Y, where
a + -1 is a real number. Find the absolute value of the Jacobian of
transform from X, Y to U, V.
(c) Find the joint probability density function for U and V. Find a for
which U and V are independent random variables. Write down fu,v (u, v)
for this a in the answer.
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