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)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a4dcd82-baf4-45bc-b40b-693a3e683492%2F01ce6904-d727-44c9-bb62-0f4132dd578b%2Fc1xk9ba_processed.jpeg&w=3840&q=75)
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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