6. The random variable X has the pdf (probability density function) given by if 0 ≤ x ≤ 1 f(x) = [kx² k(2-x) if 1 < x≤2 (a) Verify the value k = makes it so that f(x) is a valid probability density function. (b) Evaluate integral(s) to compute P(X < 1.5). Round your answer to 2 decimal places. (c) Evaluate integral(s) to compute E(X). Round your answer to 2 decimal places.
6. The random variable X has the pdf (probability density function) given by if 0 ≤ x ≤ 1 f(x) = [kx² k(2-x) if 1 < x≤2 (a) Verify the value k = makes it so that f(x) is a valid probability density function. (b) Evaluate integral(s) to compute P(X < 1.5). Round your answer to 2 decimal places. (c) Evaluate integral(s) to compute E(X). Round your answer to 2 decimal places.
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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Transcribed Image Text:6. The random variable X has the pdf (probability density function) given by
if 0 ≤ x ≤ 1
k(2-x) if 1<x<2
f(x) =
(a) Verify the value k = makes it so that f(x) is a valid probability density function.
(b) Evaluate integral(s) to compute P(X < 1.5). Round your answer to 2 decimal places.
Give Allvaron
GT Gain
(c) Evaluate integral(s) to compute E(X). Round your answer to 2 decimal places.
(d) Evaluate integral(s) to compute Var (X). Round your answer to 2 decimal places.
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