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)
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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
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1239419b-9a0e-4d7d-b530-178e8148fbce%2Ff9b278c0-81bc-44f6-ae4b-059f85230955%2Ffe8r9j9_processed.jpeg&w=3840&q=75)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1239419b-9a0e-4d7d-b530-178e8148fbce%2Ff9b278c0-81bc-44f6-ae4b-059f85230955%2Fgmco9wr_processed.png&w=3840&q=75)
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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