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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12050043-4d02-4d31-b9b4-7dfbc30a9c5d%2F8b2bad60-2d42-47fd-847b-ae7b65609772%2Fuw187bc_processed.png&w=3840&q=75)
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
Step by step
Solved in 5 steps with 3 images
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