Suppose that the random variables X and Y have a joint probability density functi f(x, y) = c(x + y)² for 0≤x≤ 1 and 0 ≤ y ≤ 1. (a) Find c. (b) Let Z = (X+Y)−¹, find E[Z]. (c) Find the marginal distribution of X and Y.

Suppose that the random variables X and Y have a joint probability density functi f(x, y) = c(x + y)² for 0≤x≤ 1 and 0 ≤ y ≤ 1. (a) Find c. (b) Let Z = (X+Y)−¹, find E[Z]. (c) Find the marginal distribution of X and Y.

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

Do A, B, and C

Suppose that the random variables X and Y have a joint probability density function
f(x, y) = c(x + y)²
for 0≤x≤ 1 and 0 ≤ y ≤ 1.
(a) Find c.
(b) Let Z = (X + Y)−¹, find E[Z].
(c) Find the marginal distribution of X and Y.
(d) What is Cov(X, Y)?
(e) Find the probability density function of X conditional on Y = 1.5.

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