Let X be continuous uniform over [0, 2] and Y be continuous unform over [3, 4]. Find and sketch the PDF of Z = X +Y, using convolutions.
Let X be continuous uniform over [0, 2] and Y be continuous unform over [3, 4]. Find and sketch the PDF of Z = X +Y, using convolutions.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
![1. Let X be continuous uniform over 0, 2] and Y be continuous unform over [3, 4].
and sketch the PDF of Z = X +Y, using convolutions.
Find
2. Let Y be exponentially distributed with parameter 1, and let Z be uniformly distributed
over the interval [0, 1]. Assume that Y and Z are independent. Find the distribution of
-Z, use convolution to find the PDF of Y – Z, and deduce that of Y
-
3. Let X be a discrete random variable with PMF px and let Y be a continuous random
variable, independent of X, with PMF fy. Derive a formula for the PDF of the random
variable X + Y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5967ae0b-1e8d-4137-907e-4e698101e1eb%2Faf38affa-0df7-4758-8c85-84f281322d92%2F2dmvqle_processed.png&w=3840&q=75)
Transcribed Image Text:1. Let X be continuous uniform over 0, 2] and Y be continuous unform over [3, 4].
and sketch the PDF of Z = X +Y, using convolutions.
Find
2. Let Y be exponentially distributed with parameter 1, and let Z be uniformly distributed
over the interval [0, 1]. Assume that Y and Z are independent. Find the distribution of
-Z, use convolution to find the PDF of Y – Z, and deduce that of Y
-
3. Let X be a discrete random variable with PMF px and let Y be a continuous random
variable, independent of X, with PMF fy. Derive a formula for the PDF of the random
variable X + Y.
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