Question: What is the variance of a continuous random variable Y with probability density function (pdf) given by g(y) = 4y^3, 0 < y < 1?
Question: What is the variance of a continuous random variable Y with probability density function (pdf) given by g(y) = 4y^3, 0 < y < 1?
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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Question: What is the variance of a continuous random variable Y with probability density function (pdf ) given by g(y) = 4y^3, 0 < y < 1?
Expert Solution
Step 1
The variance of Y, denoted by Var(Y), is defined as the expected value of the squared deviation from the mean and can be calculated as follows:
Var(Y) = E((Y - E(Y))^2) = E(Y^2) - (E(Y))^2
= ∫y^2 * g(y) dy - (E(Y))^2
= ∫y^2 * 4y^3 dy - (E(Y))^2
= ∫4y^5 dy - (E(Y))^2
= y^6/6 | from 0 to 1
= (1^6)/6 - (0^6)/6
= 1/6 - 0
= 1/6
So the variance of Y is 1/6.
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