he joint frequency function of ( X , Y) is given to be f(x, y) = Ae−x−y , ; 0 ≤ x ≤ y, 0 ≤ y < +∞ = 0 ; otherwise (i) Determine A. (ii) Find the marginal density function of X. (iii) Find the marginal density function of Y.

he joint frequency function of ( X , Y) is given to be f(x, y) = Ae−x−y , ; 0 ≤ x ≤ y, 0 ≤ y < +∞ = 0 ; otherwise (i) Determine A. (ii) Find the marginal density function of X. (iii) Find the marginal density function of Y.

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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Question

The joint frequency function of ( X , Y) is given to be f(x, y) = Ae−x−y

, ; 0 ≤ x ≤ y, 0 ≤ y < +∞ = 0 ;

otherwise
(i) Determine A.
(ii) Find the marginal density function of X.
(iii) Find the marginal density function of Y.
(iv) Examine if X and Y are independent.
(v) Find the conditional density function of Y given X = 2.

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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