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2. A random variable X has a probability density function (pdf) given by , 0< x < 1, f(x) = c, 1

2. A random variable X has a probability density function (pdf) given by , 0< x < 1, f(x) = c, 1

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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2. A random variable X has a probability density function (pdf) given by , 0< x < 1, 2 f(x) = C, 1<x < 3, 0, elsewhere, for some real constant c. (a) Determine the value of the constant c and sketch the graph of f(x). In the following questions, replace c by its numerical value computed in (a). (b) Find the cumulative distribution function (cdf) F(x) of X, and sketch its graph. (c) Find P(X < ). (d) Find P( < X < ). (e) What is P(X = 1)? %| (f) Find the moment-generating function (mgf) Mx(t) of X. Justify why it is well defined for any real finite value of t. (f) Find the moment-generating function (mgf) Mx(t) of X. Justify why it is well defined for any real finite value of t. (g) Find the 75th percentile of the distribution. Namely, find the value of T0.75 SO that P(X < Τ0.75)F(T0.T3)0.75. (h) Find the conditional probability P(X > |X > ).
Transcribed Image Text:2. A random variable X has a probability density function (pdf) given by , 0< x < 1, 2 f(x) = C, 1<x < 3, 0, elsewhere, for some real constant c. (a) Determine the value of the constant c and sketch the graph of f(x). In the following questions, replace c by its numerical value computed in (a). (b) Find the cumulative distribution function (cdf) F(x) of X, and sketch its graph. (c) Find P(X < ). (d) Find P( < X < ). (e) What is P(X = 1)? %| (f) Find the moment-generating function (mgf) Mx(t) of X. Justify why it is well defined for any real finite value of t. (f) Find the moment-generating function (mgf) Mx(t) of X. Justify why it is well defined for any real finite value of t. (g) Find the 75th percentile of the distribution. Namely, find the value of T0.75 SO that P(X < Τ0.75)F(T0.T3)0.75. (h) Find the conditional probability P(X > |X > ).
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