h. By completing the square, re-express fx,y (x, y) in the form fx,y(x, y) = e-(ax-by)² e-cy², Where a, b, c are constants. Note the difference between this expression and the original expression is that the second factor in this expression is a function of y and not of x. i. Find fy (y) using a technique similar to that you used in a.
h. By completing the square, re-express fx,y (x, y) in the form fx,y(x, y) = e-(ax-by)² e-cy², Where a, b, c are constants. Note the difference between this expression and the original expression is that the second factor in this expression is a function of y and not of x. i. Find fy (y) using a technique similar to that you used in a.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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J) use your answer in i to find E[Y] and Var[Y] 
![1. Suppose X and Y are jointly distributed with pdf fx,y(x, y), where
fx,y (x, y) = = e-(x−y)² e-x²
TT
Note that
fx(x) = √²/e-(x−y) ²e-x² dy.
TT](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa86feb48-aed4-4133-a748-653f8a12a813%2Fb785e09b-f6b4-481b-96fa-2137bbb8e820%2Fmnxrfv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Suppose X and Y are jointly distributed with pdf fx,y(x, y), where
fx,y (x, y) = = e-(x−y)² e-x²
TT
Note that
fx(x) = √²/e-(x−y) ²e-x² dy.
TT
![h. By completing the square, re-express fx,y (x, y) in the form
fx,y(x, y) = e-(ax-by)² e−cy²,
TT
Where a, b, c are constants. Note the difference between this expression and
the original expression is that the second factor in this expression is a
function of y and not of x.
i. Find fy (y) using a technique similar to that you used in a.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa86feb48-aed4-4133-a748-653f8a12a813%2Fb785e09b-f6b4-481b-96fa-2137bbb8e820%2Fp52jl2h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:h. By completing the square, re-express fx,y (x, y) in the form
fx,y(x, y) = e-(ax-by)² e−cy²,
TT
Where a, b, c are constants. Note the difference between this expression and
the original expression is that the second factor in this expression is a
function of y and not of x.
i. Find fy (y) using a technique similar to that you used in a.
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