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Suppose that X, Y are iid continuous uniform distributions over the interval (0, 1). Find the pdf of Z = X + 2Y.

Suppose that X, Y are iid continuous uniform distributions over the interval (0, 1). Find the pdf of Z = X + 2Y.

A First Course in Probability (10th Edition)
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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This revolves around the subject of linear models. The given problem is: Suppose that X, Y are iid continuous uniform distributions over the interval (0, 1). Find the pdf of Z = X + 2Y. My attempt at the problem is shown below. Is my solution correct? If not, why? I figured that the 2 in X + 2Y was a constant, so it could be ignored.

4. Suppose that X, Y are iid continuous uniform distributions over the interval (0₁1). Find pdf of 2=X+24 • X.Y: independently uniformally dorikated over (0.1) -range of X + 2Y: (02) - Let X+2Y=Z .For any 0 <=< 1, • f(x+2r) (2) = √∞00 £x(x) {y (2-x) dx = So 1dx=2 • For any 1≤2≤2 • fcx+2y) (2) = 5-00 £x (x) fy(2-x) dx = √²-1) 10x. 1cx= •{(x+2y) (Z) = Z graph of paf 02241 32-2, 1<z≤2 elsewhere 2 f(z) # →X 1-(2-1)=2=2
Transcribed Image Text:4. Suppose that X, Y are iid continuous uniform distributions over the interval (0₁1). Find pdf of 2=X+24 • X.Y: independently uniformally dorikated over (0.1) -range of X + 2Y: (02) - Let X+2Y=Z .For any 0 <=< 1, • f(x+2r) (2) = √∞00 £x(x) {y (2-x) dx = So 1dx=2 • For any 1≤2≤2 • fcx+2y) (2) = 5-00 £x (x) fy(2-x) dx = √²-1) 10x. 1cx= •{(x+2y) (Z) = Z graph of paf 02241 32-2, 1<z≤2 elsewhere 2 f(z) # →X 1-(2-1)=2=2
Suppose that X, Y are iid continuous uniform distributions over the interval (0, 1). Find the pdf of Z = X + 2Y.
Transcribed Image Text:Suppose that X, Y are iid continuous uniform distributions over the interval (0, 1). Find the pdf of Z = X + 2Y.
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