c) Let S and T be two independent random variables with probability density functions 1 f(s) =- s > 0, e elsewhere. 1 02 e t > 0, f(t) = 0. elsewhere. Given X = S+ Y and Y = T. Find a joint probability distribution function of X and Y. Then determine the marginal density function of Y.

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
Section13.1: Continuous Probability Models
Problem 3E
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c) Let S and T be two independent random variables with probability density functions
1
f(s)= -
s > 0,
e
elsewhere.
(e) =
t > 0,
e
0.
elsewhere.
Given X = S+ Y and Y = T. Find a joint probability distribution function of X and Y. Then
determine the marginal density function of Y.
Transcribed Image Text:c) Let S and T be two independent random variables with probability density functions 1 f(s)= - s > 0, e elsewhere. (e) = t > 0, e 0. elsewhere. Given X = S+ Y and Y = T. Find a joint probability distribution function of X and Y. Then determine the marginal density function of Y.
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,