Let X and Y have the joint pdf:x+y,fx,y (x, y) = { 0,0≤x≤ 1,0 ≤ y ≤ 1;otherwise.(a) Determine the marginal probability density function of Y [fy (y)](b) DetermineP(X+Y<1/2)(c) Determine E(X)

Here use given joint probability distribution of x and y.

Answered: (a) Determine the marginal probability…

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(a) Determine the marginal probability density function of Y [fy (y)] (b) Determine P(X+Y<1/2) (c) Determine E(X)

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

Let X and Y have the joint pdf:
x+y,
fx,y (x, y) = { 0,
0≤x≤ 1,0 ≤ y ≤ 1;
otherwise.
(a) Determine the marginal probability density function of Y [fy (y)]
(b) Determine
P(X+Y<1/2)
(c) Determine E(X)

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Follow-up Question

(d) Determine E(X|Y = y)
(e) Determine var(X)
(f) Determine var(X|Y = y)
(g) Determine corr(X,Y)

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