The continuous random variable X has the pdf f(x) = { (a) Find the cdf F of X. 0 x -2 if x < 1 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. 0 x -2 if x < 1 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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![### Problem Description
The continuous random variable \( X \) has the probability density function (pdf)
\[ f(x) =
\begin{cases}
0 & \text{if } x < 1 \\
x^{-2} & \text{if } x \geq 1
\end{cases}
\]
#### Questions
**(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%2F4170b34c-0f85-4584-81cf-ce7119ecbec8%2F1dyh63u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Description
The continuous random variable \( X \) has the probability density function (pdf)
\[ f(x) =
\begin{cases}
0 & \text{if } x < 1 \\
x^{-2} & \text{if } x \geq 1
\end{cases}
\]
#### Questions
**(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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