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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). d) Find P(X ≥ 3/4).

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). d) Find P(X ≥ 3/4).

MATLAB: An Introduction with Applications
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 \( f(x) = 2(1-x) \), \( 0 \leq x \leq 1 \), 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 \( P(X \geq 3/4) \).
Transcribed Image Text: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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