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4 continuous random variable X the cumulative distribution functionF(x) given by 1 0

4 continuous random variable X the cumulative distribution functionF(x) given by 1 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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A continuous random variable \( X \) has the cumulative distribution function \( F(x) \) given by \[ F(x) = \begin{cases} 0 & x \leq 0 \\ \frac{1}{2}x^2 & 0 < x < 1 \\ 2x - \frac{1}{2}x^2 - 1 & 1 \leq x < 2 \\ 1 & x \geq 2 \end{cases} \] - Find the density function \( f(x) \). - Find \( P(0 < X < 1.5) \). - Find the expectation \( E(4X - 5) \).
Transcribed Image Text:A continuous random variable \( X \) has the cumulative distribution function \( F(x) \) given by \[ F(x) = \begin{cases} 0 & x \leq 0 \\ \frac{1}{2}x^2 & 0 < x < 1 \\ 2x - \frac{1}{2}x^2 - 1 & 1 \leq x < 2 \\ 1 & x \geq 2 \end{cases} \] - Find the density function \( f(x) \). - Find \( P(0 < X < 1.5) \). - Find the expectation \( E(4X - 5) \).
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