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Page 173, 3.2.16.* Let X and Y and have joint probability 2-Xe-3 , y = 0, 1,..., ∞, x = 0, 1, 2, ..., y, f(x, y)= {x!(y-x)!' 0, elsewhere. (a) Find the joint moment generating function M(t₁, t₂). (b) Compute the correlation coefficient of X and Y.

Page 173, 3.2.16.* Let X and Y and have joint probability 2-Xe-3 , y = 0, 1,..., ∞, x = 0, 1, 2, ..., y, f(x, y)= {x!(y-x)!' 0, elsewhere. (a) Find the joint moment generating function M(t₁, t₂). (b) Compute the correlation coefficient of X and Y.

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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please answer only page 173 3.2.16

Page 173, 3.2.16.* Let X and Y and have joint probability ma 2-te-3 , y = 0, 1,..., ∞, x = 0, 1, 2,..., y, f (x, y) = {x!(y=x)!' 0, elsewhere. (a) Find the joint moment generating function M(t₁, t₂). (b) Compute the correlation coefficient of X and Y.
Transcribed Image Text:Page 173, 3.2.16.* Let X and Y and have joint probability ma 2-te-3 , y = 0, 1,..., ∞, x = 0, 1, 2,..., y, f (x, y) = {x!(y=x)!' 0, elsewhere. (a) Find the joint moment generating function M(t₁, t₂). (b) Compute the correlation coefficient of X and Y.
Expert Solution
Step 1

Given that,

X and Y have a joint probability mass function fx,y.

fx,y=2y-xe-3x!y-x!, y=0,1,2,...,∞ ; x=0,1,2,...,y=0                  otherwise

Need to obtain:

(a) The joint moment generating function Mt1,t2 of X and Y.

(b) The correlation coefficient of X and Y.

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