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The random variables X and Y have joint probability density function f(x, y) = { 1"y(3x + y), 0

The random variables X and Y have joint probability density function f(x, y) = { 1"y(3x + y), 0

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The random variables X and Y have joint probability density function (ry(3x + y), 0 <x < 2, 0 < y <1 0, f(x, y) = otherwise i) Calculate P(0.6 < X < 1.8). Give your answer to one decimal place. i) Calculate P(0.4 <Y< 0.9). Give your answer to two decimal places. ii) Calculate E(4X – 2). Give your answer to two decimal places. [Hint: find E(X) to two decimal places]. iv) Calculate Var(2Y – 1). Give your answer to one decimal place. [Hint: find E(Y), E(Y²) and Var(Y) to two decimal places]. v) Given E(XY) =1 and E(Y) = 0.68, calculate Cov(X,Y). Give your answer to three decimal places. [Hint: find E(X) to two decimal places].
Transcribed Image Text:The random variables X and Y have joint probability density function (ry(3x + y), 0 <x < 2, 0 < y <1 0, f(x, y) = otherwise i) Calculate P(0.6 < X < 1.8). Give your answer to one decimal place. i) Calculate P(0.4 <Y< 0.9). Give your answer to two decimal places. ii) Calculate E(4X – 2). Give your answer to two decimal places. [Hint: find E(X) to two decimal places]. iv) Calculate Var(2Y – 1). Give your answer to one decimal place. [Hint: find E(Y), E(Y²) and Var(Y) to two decimal places]. v) Given E(XY) =1 and E(Y) = 0.68, calculate Cov(X,Y). Give your answer to three decimal places. [Hint: find E(X) to two decimal places].
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