**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.

Answered: 4. The pdf of X is f(x) = 24 (27 - x³)…

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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