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).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 21E
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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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb41de797-8c36-43f3-a49e-0d77bbbd163e%2Fcceb30bb-1054-4db2-b4a2-1f7245b46e7a%2F7azoqux_processed.jpeg&w=3840&q=75)
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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