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.
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 29CR
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