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3. Let X be a continuous random variable with PDF: f(x) = 2x/9 for 0

3. Let X be a continuous random variable with PDF: f(x) = 2x/9 for 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Let X be a continuous random variable with PDF: f(x) = 2x/9 for 0<x<3. Let Y = 2x+1, Using the Change of Variable Formula, what is the Cumulative Distribution Function of Y? O a) G(y) = 2(y-1)219 O b) G(y) = (y-1)/18 O c) G(y) = (y-1)2/36 O d) G(y) = y(y-2)/18 4. Suppose X and Y are continuous random variables with the joint PDF f(x,y) = (x + 2y)/4, where 0 < x< 2 and 0 <y < 1. What is the marginal PDF of X? O a) f(x) = x/4 + 1/4 O b) f(x) = x + 1/4 O c) f(x) = (x2 + 2xy)/6 O d) f(x) = x/3 + 1/3
Transcribed Image Text:3. Let X be a continuous random variable with PDF: f(x) = 2x/9 for 0<x<3. Let Y = 2x+1, Using the Change of Variable Formula, what is the Cumulative Distribution Function of Y? O a) G(y) = 2(y-1)219 O b) G(y) = (y-1)/18 O c) G(y) = (y-1)2/36 O d) G(y) = y(y-2)/18 4. Suppose X and Y are continuous random variables with the joint PDF f(x,y) = (x + 2y)/4, where 0 < x< 2 and 0 <y < 1. What is the marginal PDF of X? O a) f(x) = x/4 + 1/4 O b) f(x) = x + 1/4 O c) f(x) = (x2 + 2xy)/6 O d) f(x) = x/3 + 1/3
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