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The random variables X and Y have joint density function f(x, y) = 2-1.2x -0.8y, 0 ≤x≤1, 0≤y≤ 1. Calculate the covariance of X and Y as Coo(X,Y) = E{(X − +x)(Y → +y) = n −ux) - HY)f(z, 8)dydz. - 0.079 X

The random variables X and Y have joint density function f(x, y) = 2-1.2x -0.8y, 0 ≤x≤1, 0≤y≤ 1. Calculate the covariance of X and Y as Coo(X,Y) = E{(X − +x)(Y → +y) = n −ux) - HY)f(z, 8)dydz. - 0.079 X

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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The random variables \( X \) and \( Y \) have joint density function \[ f(x, y) = 2 - 1.2x - 0.8y, \quad 0 \leq x \leq 1, \quad 0 \leq y \leq 1. \] Calculate the covariance of \( X \) and \( Y \) as \[ \text{Cov}(X, Y) = E[(X - \mu_X)(Y - \mu_Y)] = \int_0^1 \int_0^1 (x - \mu_X)(y - \mu_Y) f(x, y) dy dx = 0.079. \] Note: You will have to first calculate \( \mu_X \) and \( \mu_Y \) as \[ \mu_X = E[X] = \int_0^1 \int_0^1 x f(x, y) dy dx, \] and \[ \mu_Y = E[Y] = \int_0^1 \int_0^1 y f(x, y) dy dx. \]
Transcribed Image Text:The random variables \( X \) and \( Y \) have joint density function \[ f(x, y) = 2 - 1.2x - 0.8y, \quad 0 \leq x \leq 1, \quad 0 \leq y \leq 1. \] Calculate the covariance of \( X \) and \( Y \) as \[ \text{Cov}(X, Y) = E[(X - \mu_X)(Y - \mu_Y)] = \int_0^1 \int_0^1 (x - \mu_X)(y - \mu_Y) f(x, y) dy dx = 0.079. \] Note: You will have to first calculate \( \mu_X \) and \( \mu_Y \) as \[ \mu_X = E[X] = \int_0^1 \int_0^1 x f(x, y) dy dx, \] and \[ \mu_Y = E[Y] = \int_0^1 \int_0^1 y f(x, y) dy dx. \]
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Step 1: Write the given information.

Given that the joint density function of X and Y is,

f open parentheses x comma y close parentheses equals 2 minus 1.2 x minus 0.8 y comma space 0 less or equal than x less or equal than 1 comma space 0 less or equal than y less or equal than 1


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