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# Nicol (see References) lets the pdf of X be defined by

ISBN: 9780321923271 41

## Solution for problem 20E Chapter 3.1

Probability and Statistical Inference | 9th Edition

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Problem 20E

Nicol (see References) lets the pdf of X be defined by

Find

(a) The value of c so that f (x) is a pdf.

(b) The mean of X (if it exists).

(c) The variance of X (if it exists).

(d) P(1/2 ≤ X ≤ 2).

Step-by-Step Solution:

Step 1 of 5</p>

Total probability =1

f(x)dx=1

+ =1

=1

½-c(0-½)=1

c=1

Step 2 of 5</p>

b)Mean=E(x)

=f(x) dx

=+

=

=⅓ -(0-1)

=⅓+1

=4/3

Step 3 of 5</p>

c) E(x2)= f(x) dx

=+

=

=1/4 -(-0)           =⅓+1

=

V(X)=E(x2)-E(x)2

=-(4/3)2

=

Hence variance does not exist

Step 4 of 5

Step 5 of 5

##### ISBN: 9780321923271

Since the solution to 20E from 3.1 chapter was answered, more than 828 students have viewed the full step-by-step answer. The answer to “Nicol (see References) lets the pdf of X be defined by Find(a) The value of c so that f (x) is a pdf.(b) The mean of X (if it exists).(c) The variance of X (if it exists).(d) P(1/2 ? X ? 2).” is broken down into a number of easy to follow steps, and 42 words. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. This full solution covers the following key subjects: exists, pdf, nicol, lets, mean. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. The full step-by-step solution to problem: 20E from chapter: 3.1 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM.

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Nicol (see References) lets the pdf of X be defined by

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