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2. The joint p.d.f. of the r.v.'s X and Y is given by ={8 (0 +6²9), 0.5 = 51, 05051 0, otherwise. fx,y(x, y) = (a) Find the marginal p.d.f.'s fx and fy and specify the range of the arguments involved. (b) Calculate E(X), E(X²), Var(X), E(Y), E(Y²), Var(Y), E(XY), Cov(X, Y) and p(X, Y). (c) Determine the conditional p.d.f's fx|y(x|y) and fy|x(y|x) and specify the range of the arguments involved.

2. The joint p.d.f. of the r.v.'s X and Y is given by ={8 (0 +6²9), 0.5 = 51, 05051 0, otherwise. fx,y(x, y) = (a) Find the marginal p.d.f.'s fx and fy and specify the range of the arguments involved. (b) Calculate E(X), E(X²), Var(X), E(Y), E(Y²), Var(Y), E(XY), Cov(X, Y) and p(X, Y). (c) Determine the conditional p.d.f's fx|y(x|y) and fy|x(y|x) and specify the range of the arguments involved.

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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Question
2. The joint p.d.f. of the r.v.'s X and Y is given by fx,y(x, y) = ſ § (x + y²), 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0, otherwise. (a) Find the marginal p.d.f.'s fx and fy and specify the range of the arguments involved. (b) Calculate E(X), E(X²), Var(X), E(Y), E(Y²), Var(Y), E(XY), Cov(X,Y) and p(X, Y). (c) Determine the conditional p.d.f's fx|y(x|y) and fy|x(y|x) and specify the range of the arguments involved. (d) Calculate the conditional probability P(Y > ½|x = 3). (e) Calculate the probability P(Y > ½). (f) Evaluate E(X|Y = y) for any fixed y with 0 ≤ y ≤ 1. (g) Evaluate E(E(XY)) and compare it with E(X). (h) Calculate the m.g.f. Mx,y.
Transcribed Image Text:2. The joint p.d.f. of the r.v.'s X and Y is given by fx,y(x, y) = ſ § (x + y²), 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0, otherwise. (a) Find the marginal p.d.f.'s fx and fy and specify the range of the arguments involved. (b) Calculate E(X), E(X²), Var(X), E(Y), E(Y²), Var(Y), E(XY), Cov(X,Y) and p(X, Y). (c) Determine the conditional p.d.f's fx|y(x|y) and fy|x(y|x) and specify the range of the arguments involved. (d) Calculate the conditional probability P(Y > ½|x = 3). (e) Calculate the probability P(Y > ½). (f) Evaluate E(X|Y = y) for any fixed y with 0 ≤ y ≤ 1. (g) Evaluate E(E(XY)) and compare it with E(X). (h) Calculate the m.g.f. Mx,y.
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