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Exercise 5.32 If X has distribution function for - 0o < x < 0, 2(1+x2) 1+ 2x2 2(1+ x2) F(x) = for 0

Exercise 5.32 If X has distribution function for - 0o < x < 0, 2(1+x2) 1+ 2x2 2(1+ x2) F(x) = 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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5.32
**Exercise 5.32:** If \( X \) has distribution function \[ F(x) = \begin{cases} \frac{1}{2(1 + x^2)} & \text{for } -\infty < x \leq 0, \\ \frac{1 + 2x^2}{2(1 + x^2)} & \text{for } 0 < x < \infty, \end{cases} \] show that \( X \) is continuous and find its density function.
Transcribed Image Text:**Exercise 5.32:** If \( X \) has distribution function \[ F(x) = \begin{cases} \frac{1}{2(1 + x^2)} & \text{for } -\infty < x \leq 0, \\ \frac{1 + 2x^2}{2(1 + x^2)} & \text{for } 0 < x < \infty, \end{cases} \] show that \( X \) is continuous and find its density function.
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