The continuous random variable X has the pdf f(x) = { (a) Find the cdf F of X. if x < 1 -2 (x-² if x ≥ 1. (b) Find the median of X, i.e., solve the equation F(x) = 1/2 (c) Give an example of a positive continuous random variable X such that E(X) is finite, but E(X2) is infinite. Justify your answer.
The continuous random variable X has the pdf f(x) = { (a) Find the cdf F of X. if x < 1 -2 (x-² if x ≥ 1. (b) Find the median of X, i.e., solve the equation F(x) = 1/2 (c) Give an example of a positive continuous random variable X such that E(X) is finite, but E(X2) is infinite. Justify your answer.
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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![**The continuous random variable \( X \) has the probability density function (pdf):**
\[
f(x) =
\begin{cases}
0 & \text{if } x < 1 \\
x^{-2} & \text{if } x \geq 1.
\end{cases}
\]
**(a) Find the cumulative distribution function (cdf) \( F \) of \( X \).**
**(b) Find the median of \( X \), i.e., solve the equation**
\[
F(x) = \frac{1}{2}.
\]
**(c) Give an example of a positive continuous random variable \( X \) such that \( E(X) \) is finite, but \( E(X^2) \) is infinite. Justify your answer.**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F017ae768-eed2-4ce7-905a-bf91d203cb59%2F761c0d91-0955-451b-95da-eb670ba5cfa9%2Fskbep1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**The continuous random variable \( X \) has the probability density function (pdf):**
\[
f(x) =
\begin{cases}
0 & \text{if } x < 1 \\
x^{-2} & \text{if } x \geq 1.
\end{cases}
\]
**(a) Find the cumulative distribution function (cdf) \( F \) of \( X \).**
**(b) Find the median of \( X \), i.e., solve the equation**
\[
F(x) = \frac{1}{2}.
\]
**(c) Give an example of a positive continuous random variable \( X \) such that \( E(X) \) is finite, but \( E(X^2) \) is infinite. Justify your answer.**
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