EBK FIRST COURSE IN PROBABILITY, A
EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753676
Author: Ross
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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Textbook Question
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Chapter 5, Problem 5.1P

Let X be a random variable with probability density function f ( x ) = { c ( 1 x 2 ) 1 < x < 0 0 otherwise

a. What is the value of c?

b. What is the cumulative distribution function of X?

Expert Solution
Check Mark
To determine

(a) To compute: To find the value of c

Answer to Problem 5.1P

The value of c is 0.75.

Explanation of Solution

Given information:

The probability density function of X

  (x)= {c (1x2)                   1<x<10                                        otherwise

Calculation:

As the probability density function integrates to 1

  11c (1x2) dx = 1

= [c × (xx33)]11 = 1

= c × (113(113)) = 1

= c × (223)=1

= c × (43)=1

  c=34=0.75

(b)

Expert Solution
Check Mark
To determine

To find: Cumulative distribution of X

Answer to Problem 5.1P

The cumulative distribution of X is  0.75 × (xx33+23) .

Explanation of Solution

Formula used:

F (x) = 1xf(t)dt

Calculation:

The cumulative distribution of X is

  = 1x0.75 × (1t2) dt

  = [0.75 × (tt33)]1x

  =0.75 × [xx33 (113)]

  =0.75 × (xx33+23)

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Chapter 5 Solutions

EBK FIRST COURSE IN PROBABILITY, A

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