3. Let the random variable \( X \) have the pdf \( f(x) = 2(1 - x) \), \( 0 \leq x \leq 1 \), zero elsewhere. a) Find the cdf of \( X \). Provide \( F(x) \) for all real numbers \( x \) (set up the appropriate cases). b) Find \( P(1/4 \leq X \leq 3/4) \). c) Find \( P(X = 3/4) \). d) Find \( P(X \geq 3/4) \).

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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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3. Let the random variable X have the pdf f(x) = 2(1-x), 0≤x≤ 1, zero elsewhere. a) Find the cdf of X. Provide F(x) for all real numbers x (set up the appropriate cases). b) Find P(1/4 ≤ x ≤ 3/4). c) Find P(X= 3/4).