Two independent random variables are defined with the following distributions: X 1 2 3 (a) Р 0.5 0.2 0.3 Y p 1 2 0.2 4 0.6 Determine the PDF of the sum of X and Y using convolutions. 0.2 (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 1 2 3 (a) Р 0.5 0.2 0.3 Y p 1 2 0.2 4 0.6 Determine the PDF of the sum of X and Y using convolutions. 0.2 (b) Determine the mean and variance of the sum by treating the result as the sum of two independent random variables.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 1CR
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Transcribed Image Text:Two independent random variables are defined with the following distributions:
Xp
Y p
1
0.5
1
0.2
2 0.2
2
0.2
3
0.3
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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