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Q7: 4.5-4. For two independent random variables X and Y show that P(Y ≤ X) = Fy(x)/x (x) dx or P(Y ≤X) = 1- Fx(y)fr(y) dy

Q7: 4.5-4. For two independent random variables X and Y show that P(Y ≤ X) = Fy(x)/x (x) dx or P(Y ≤X) = 1- Fx(y)fr(y) dy

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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Prob ... solve Q 7 & Q 8
Q5: Two random variables X and Y have a joint density fx, y(x, y)=[u(x) - u(x-4)]u(y) y³ exp[-(x + 1)²] Find the marginal densities and distributions of X and Y. Q6: 4.5-3. Given the joint distribution function Q8: Fx, y(x, y) = u(x)u(y)[l-e-a-e-ay+e-ax+] find: (a) The conditional density functions fx(x|Y=y) and fy(y)X = x). (b) Are the random variables X and Y statistically independent? Q7: 4.5-4. For two independent random variables X and Y show that PY ≤X) = x) = [*_ Fr(x) x(x) dx 88 or P(Y ≤X) = 1- Fx (1) fy(y) dy 4.5-5. Two random variables X and Y have a joint probability density function. x²y 0<y<x<2 elsewhere fx.y(x, y) = 16 (a) Find the marginal density functions of X and Y. (b) Are X and Y statistically independent?
Transcribed Image Text:Q5: Two random variables X and Y have a joint density fx, y(x, y)=[u(x) - u(x-4)]u(y) y³ exp[-(x + 1)²] Find the marginal densities and distributions of X and Y. Q6: 4.5-3. Given the joint distribution function Q8: Fx, y(x, y) = u(x)u(y)[l-e-a-e-ay+e-ax+] find: (a) The conditional density functions fx(x|Y=y) and fy(y)X = x). (b) Are the random variables X and Y statistically independent? Q7: 4.5-4. For two independent random variables X and Y show that PY ≤X) = x) = [*_ Fr(x) x(x) dx 88 or P(Y ≤X) = 1- Fx (1) fy(y) dy 4.5-5. Two random variables X and Y have a joint probability density function. x²y 0<y<x<2 elsewhere fx.y(x, y) = 16 (a) Find the marginal density functions of X and Y. (b) Are X and Y statistically independent?
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