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Justify and explain that if X and Y are independent random variables with respective parameters lambda 1 and lambda 2, calculate the conditional distribution of X given that X+Y=n

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

Justify and explain that if X and Y are independent random variables with respective parameters lambda 1 and lambda 2, calculate the conditional distribution of X given that X+Y=n

Expert Solution

Step 1

It is provided that X+Y = n and X, Y are non-negative, then X can choose 1, …, n.

Therefore,

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