1. Let X be a continuous random variable with cdf 0, x≤0 x² F(x)= = 7,0 ≤ x < 2 1, 2≤x a. Find P(X ≤ 1), P(1 ≤X ≤ 1.5) and P(X>1.5). b. Derive the pdf of X. c. Find the median and 75th percentile of the random variable.
1. Let X be a continuous random variable with cdf 0, x≤0 x² F(x)= = 7,0 ≤ x < 2 1, 2≤x a. Find P(X ≤ 1), P(1 ≤X ≤ 1.5) and P(X>1.5). b. Derive the pdf of X. c. Find the median and 75th percentile of the random variable.
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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![1. Let \( X \) be a continuous random variable with cumulative distribution function (cdf)
\[
F(x) =
\begin{cases}
0, & x \leq 0 \\
\frac{x^2}{4}, & 0 \leq x < 2 \\
1, & 2 \leq x
\end{cases}
\]
a. Find \( P(X \leq 1) \), \( P(1 \leq X \leq 1.5) \), and \( P(X > 1.5) \).
b. Derive the probability density function (pdf) of \( X \).
c. Find the median and 75th percentile of the random variable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5dfcde0a-cc8e-4f7e-b5e2-9ec6ad36a3c9%2F89f2fe93-5cbf-4f82-8a56-21bbf8648d5f%2Fj3merc3_processed.png&w=3840&q=75)
Transcribed Image Text:1. Let \( X \) be a continuous random variable with cumulative distribution function (cdf)
\[
F(x) =
\begin{cases}
0, & x \leq 0 \\
\frac{x^2}{4}, & 0 \leq x < 2 \\
1, & 2 \leq x
\end{cases}
\]
a. Find \( P(X \leq 1) \), \( P(1 \leq X \leq 1.5) \), and \( P(X > 1.5) \).
b. Derive the probability density function (pdf) of \( X \).
c. Find the median and 75th percentile of the random variable.
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