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Q 4.1. Suppose X and Y are independent random variables, which are jointly continuous. 1. Show carefully that the distribution of 'X + Y given X = x' is equal to the distribution of the random variable x + Y. Hint: Consider the change of variables h(x, y) = (x,x+y).

Q 4.1. Suppose X and Y are independent random variables, which are jointly continuous. 1. Show carefully that the distribution of 'X + Y given X = x' is equal to the distribution of the random variable x + Y. Hint: Consider the change of variables h(x, y) = (x,x+y).

A First Course in Probability (10th Edition)
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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Q 4.1. Suppose X and Y are independent random variables, which are jointly continuous. 1. Show carefully that the distribution of ‘X + Y given X = x' is equal to the distribution of the random variable x + Y. Hint: Consider the change of variables h(x, y) = (x,x+y).
Transcribed Image Text:Q 4.1. Suppose X and Y are independent random variables, which are jointly continuous. 1. Show carefully that the distribution of ‘X + Y given X = x' is equal to the distribution of the random variable x + Y. Hint: Consider the change of variables h(x, y) = (x,x+y).
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