Let X be a random variable with probability density function f(x) = {cx", 00 F(x) = P(X < x) = { 1-e-x*, 1/2

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Chapter1: Combinatorial Analysis
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Let X be a random variable with probability density function
(cx", 0<x < 1,
f(x) = {"0,"
%3D
otherwise
(a) What is the value of c ?
(b) What is the cumulative distribution function F(x) ?
wwW.
Suppose that the cumulative distribution function of X is given by
www
0,
x <0
4'
0<x < 1
F(x) = P(X < x) = {5+
1< x < 2
4
2 < x < 3
12'
1,
x 2 3
Find P < x < 3}.
Suppose that the cumulative distribution function of the random variable X
is given by
F(x) = P(X < x) =-
1- e-x,
x>0
0,
Calculate P(X > 1).
Transcribed Image Text:Let X be a random variable with probability density function (cx", 0<x < 1, f(x) = {"0," %3D otherwise (a) What is the value of c ? (b) What is the cumulative distribution function F(x) ? wwW. Suppose that the cumulative distribution function of X is given by www 0, x <0 4' 0<x < 1 F(x) = P(X < x) = {5+ 1< x < 2 4 2 < x < 3 12' 1, x 2 3 Find P < x < 3}. Suppose that the cumulative distribution function of the random variable X is given by F(x) = P(X < x) =- 1- e-x, x>0 0, Calculate P(X > 1).
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