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Let X be a random variable with pdf f(x) = 3(1 – x)² when 0 <æ < 1, and f(x) = 0 otherwise a. Verify that f is a valid pdf. b. Find the mean and variance of X.

Let X be a random variable with pdf f(x) = 3(1 – x)² when 0 <æ < 1, and f(x) = 0 otherwise a. Verify that f is a valid pdf. b. Find the mean and variance of X.

MATLAB: An Introduction with Applications
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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Let X be a random variable with pdf f(x) = 3(1 – x)? when 0 < x< 1, and f(x) = 0 otherwise. a. Verify that f is a valid pdf. b. Find the mean and variance of X. c. Find P(X < 1/2). d. Find P(X < 1/2| X > 1/4).
Transcribed Image Text:Let X be a random variable with pdf f(x) = 3(1 – x)? when 0 < x< 1, and f(x) = 0 otherwise. a. Verify that f is a valid pdf. b. Find the mean and variance of X. c. Find P(X < 1/2). d. Find P(X < 1/2| X > 1/4).
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Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case you require the unanswered parts also, kindly re-post that parts separately.

Let X be a random variable with fx=31-x2, 0≤x≤1

a.

Condition for valid density: ∫01fxdx=1

Consider,

∫01fxdx=∫0131-x2dx                =31-x3-1301              =-0-1               =1

Hence, f(x) is a valid density function.

 

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