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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Answered: 1. Let X be a continuous random…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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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.