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a random variable whose pdf is the form of f(x) = Cxm(1-x) where x E (0, 1) and m is a non-negative integer. (a) Consider the special situation of m = 1. Find the value of C such that the pdf is a proper pdf. (b) Argue that for a general m, the pdf must be f(x) = (m + 1)(m + 2)a"(1 – x) for x E (0, 1). %3D (c) Show that the cumulative distribution function (CDF) of X is

a random variable whose pdf is the form of f(x) = Cxm(1-x) where x E (0, 1) and m is a non-negative integer. (a) Consider the special situation of m = 1. Find the value of C such that the pdf is a proper pdf. (b) Argue that for a general m, the pdf must be f(x) = (m + 1)(m + 2)a"(1 – x) for x E (0, 1). %3D (c) Show that the cumulative distribution function (CDF) of X is

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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a random variable whose pdf is the form of f(x) = Cxm(1-x) where x E (0, 1) and m is a non-negative integer. (a) Consider the special situation of m = 1. Find the value of C such that the pdf is a proper pdf. (b) Argue that for a general m, the pdf must be f (x) = (m + 1)(m + 2)x"(1 – x) for x E (0, 1). (c) Show that the cumulative distribution function (CDF) of X is pm+1 xm+2 F(x) (m+1)(m + 2) — т +1 m + 2 (d) Continue from part (c). Evaluate the CDF at -1, 0.5, and 2 i.e., find F(-1), F(0.5), and F(2). Be careful and think twice about your answers. (e) In this class, we haven't studied the concept of expectation. For a continuous random variable X, its expectation is defined as E[X] = [ xf(x)dx. Find E[X].
Transcribed Image Text:a random variable whose pdf is the form of f(x) = Cxm(1-x) where x E (0, 1) and m is a non-negative integer. (a) Consider the special situation of m = 1. Find the value of C such that the pdf is a proper pdf. (b) Argue that for a general m, the pdf must be f (x) = (m + 1)(m + 2)x"(1 – x) for x E (0, 1). (c) Show that the cumulative distribution function (CDF) of X is pm+1 xm+2 F(x) (m+1)(m + 2) — т +1 m + 2 (d) Continue from part (c). Evaluate the CDF at -1, 0.5, and 2 i.e., find F(-1), F(0.5), and F(2). Be careful and think twice about your answers. (e) In this class, we haven't studied the concept of expectation. For a continuous random variable X, its expectation is defined as E[X] = [ xf(x)dx. Find E[X].
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