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Two independent random variables are defined with the following distributions: X p 1 2 3 (a) 0.5 0.2 0.3 Y p 1 2 4 0.2 0.2 0.6 Determine the PDF of the sum of X and Y using convolutions. (b) Determine the mean and variance of the sum by treating the result as the sum of two independent random variables.

Two independent random variables are defined with the following distributions: X p 1 2 3 (a) 0.5 0.2 0.3 Y p 1 2 4 0.2 0.2 0.6 Determine the PDF of the sum of X and Y using convolutions. (b) Determine the mean and variance of the sum by treating the result as the sum of two independent random variables.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Two independent random variables are defined with the following distributions:** | X | p | |---|----| | 1 | 0.5| | 2 | 0.2| | 3 | 0.3| | Y | p | |---|----| | 1 | 0.2| | 2 | 0.2| | 4 | 0.6| (a) Determine the PDF of the sum of \( X \) and \( Y \) using convolutions. (b) Determine the mean and variance of the sum by treating the result as the sum of two independent random variables.
Transcribed Image Text:**Two independent random variables are defined with the following distributions:** | X | p | |---|----| | 1 | 0.5| | 2 | 0.2| | 3 | 0.3| | Y | p | |---|----| | 1 | 0.2| | 2 | 0.2| | 4 | 0.6| (a) Determine the PDF of the sum of \( X \) and \( Y \) using convolutions. (b) Determine the mean and variance of the sum by treating the result as the sum of two independent random variables.
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