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4. The pdf of X is f(x) = 24 (27 - x³) for 0 < x < 3, and 0 otherwise. a) Find P(1 < X < 2). b) Find E(X). c) Find the third moment of X.

4. The pdf of X is f(x) = 24 (27 - x³) for 0 < x < 3, and 0 otherwise. a) Find P(1 < X < 2). b) Find E(X). c) Find the third moment 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
Section: Chapter Questions
Problem 1P
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**Problem 4** The probability density function (pdf) of \( X \) is given by: \[ f(x) = \frac{4}{243}(27 - x^3) \quad \text{for } 0 < x < 3, \text{ and } 0 \text{ otherwise}. \] **Tasks:** a) Calculate \( P(1 < X < 2) \). b) Determine \( E(X) \), the expected value of \( X \). c) Find the third moment of \( X \). d) Compute \( E[X(2X^2 - 3) + 10] \). In this problem, you will explore the properties of the given pdf over a specified range and compute various statistical measures by integration.
Transcribed Image Text:**Problem 4** The probability density function (pdf) of \( X \) is given by: \[ f(x) = \frac{4}{243}(27 - x^3) \quad \text{for } 0 < x < 3, \text{ and } 0 \text{ otherwise}. \] **Tasks:** a) Calculate \( P(1 < X < 2) \). b) Determine \( E(X) \), the expected value of \( X \). c) Find the third moment of \( X \). d) Compute \( E[X(2X^2 - 3) + 10] \). In this problem, you will explore the properties of the given pdf over a specified range and compute various statistical measures by integration.
Expert Solution
Step 1: Understanding the problem

As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted.


The pdf of X 

f(x)=4/243(27-x3)        for 0<x<3 

0                                   Otherwise 

We have to find

a.. P(1<X<2)

b.. E(X) 

c.. Third moment of X 

steps

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