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Problem 14 Let X be a random variable with the following CDF for a <0 for 0

Problem 14 Let X be a random variable with the following CDF for a <0 for 0

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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**Problem 14** Let \( X \) be a random variable with the following CDF: \[ F_X(x) = \begin{cases} 0 & \text{for } x < 0 \\ x & \text{for } 0 \leq x < \frac{1}{4} \\ x + \frac{1}{2} & \text{for } \frac{1}{4} \leq x < \frac{1}{2} \\ 1 & \text{for } x \geq \frac{1}{2} \end{cases} \] a. Find the generalized PDF of \( X, f_X(x) \). b. Find \( E[X] \) using \( f_X(x) \). c. Find \( \text{Var}(X) \) using \( f_X(x) \).
Transcribed Image Text:**Problem 14** Let \( X \) be a random variable with the following CDF: \[ F_X(x) = \begin{cases} 0 & \text{for } x < 0 \\ x & \text{for } 0 \leq x < \frac{1}{4} \\ x + \frac{1}{2} & \text{for } \frac{1}{4} \leq x < \frac{1}{2} \\ 1 & \text{for } x \geq \frac{1}{2} \end{cases} \] a. Find the generalized PDF of \( X, f_X(x) \). b. Find \( E[X] \) using \( f_X(x) \). c. Find \( \text{Var}(X) \) using \( f_X(x) \).
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