7. If X is a random variable with fx Let Y = 3√In X. (a) Fx(x) ) = 1, 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem Statement:**
Given a random variable \( X \) with the probability density function:
\[ f_X(x) = \frac{1}{x}, \quad 1 < x < e. \]
We define a new variable \( Y \) as:
\[ Y = 3\sqrt{\ln X}. \]
**Questions:**
(a) Find the cumulative distribution function \( F_X(x) \).
(b) Find the cumulative distribution function \( F_Y(y) \).
(c) Find the probability density function \( f_Y(y) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30e714d6-c3d6-4fe9-9c10-b4b8c64f125f%2F3ea95b18-49c2-41bb-847b-e09ce8747d02%2Faej3u9o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given a random variable \( X \) with the probability density function:
\[ f_X(x) = \frac{1}{x}, \quad 1 < x < e. \]
We define a new variable \( Y \) as:
\[ Y = 3\sqrt{\ln X}. \]
**Questions:**
(a) Find the cumulative distribution function \( F_X(x) \).
(b) Find the cumulative distribution function \( F_Y(y) \).
(c) Find the probability density function \( f_Y(y) \).
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