A continuous random variable X has p.d.f. 5x-6, for x > 1 f(x) = 0, Suppose Y = . (a) Determine the c.d.f. of Y, that is G(y) (h) Find thendf of Y otherwise.
A continuous random variable X has p.d.f. 5x-6, for x > 1 f(x) = 0, Suppose Y = . (a) Determine the c.d.f. of Y, that is G(y) (h) Find thendf of Y otherwise.
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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Please answer both parts of the question clearly thanks
![**Problem Statement:**
Consider a continuous random variable \( X \) with probability density function (p.d.f.) given by:
\[
f(x) =
\begin{cases}
5x^{-6}, & \text{for } x > 1 \\
0, & \text{otherwise.}
\end{cases}
\]
Suppose \( Y = \frac{1}{X} \).
**Tasks:**
(a) Determine the cumulative distribution function (c.d.f.) of \( Y \), denoted as \( G(y) \).
(b) Find the probability density function (p.d.f.) of \( Y \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8d46346-fe9f-45aa-a3a0-df12b7cae379%2Fd7c168fc-70bc-4607-8e19-b899174af208%2Fc6u18xe_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Consider a continuous random variable \( X \) with probability density function (p.d.f.) given by:
\[
f(x) =
\begin{cases}
5x^{-6}, & \text{for } x > 1 \\
0, & \text{otherwise.}
\end{cases}
\]
Suppose \( Y = \frac{1}{X} \).
**Tasks:**
(a) Determine the cumulative distribution function (c.d.f.) of \( Y \), denoted as \( G(y) \).
(b) Find the probability density function (p.d.f.) of \( Y \).
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