   # Consider the following exponential probability density function. f ( x ) = 1 3 e − x / 3 f o r x ≥ 0 a. Write the formula for P ( x ≤ x 0 ). b. Find P ( x ≤ 2). c. Find P ( x ≥ 3). d. Find P ( x ≤ 5). e. Find P (2 ≤ x ≤ 5). 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 6.4, Problem 33E
Textbook Problem
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## Consider the following exponential probability density function. f ( x ) = 1 3 e − x / 3       f o r   x ≥ 0 a. Write the formula for P(x ≤ x0). b. Find P(x ≤ 2). c. Find P(x ≥ 3). d. Find P(x ≤ 5). e. Find P(2 ≤ x ≤ 5).

a.

To determine

Find the formula for P(xx0).

### Explanation of Solution

Calculation:

The variable x follows exponential probability distribution. The exponential probability density function is,

f(x)=13ex/3  for x0.

The cumulative probability density function is,

P(xx0)

b.

To determine

Compute the value of P(x2).

c.

To determine

Compute the value of P(x3).

d.

To determine

Compute the value of P(x5).

e.

To determine

Compute the value of P(2x5).

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