   Chapter 9.2, Problem 35E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

# Using the Exponential Density Function In Exercises 33-36, find the required probabilities using the exponential probability density function f ( t ) 1 λ e − t / λ , [ 0 , ∞ ) .Useful Life The lifetime t (in years) of a battery is exponentially distributed with λ   =   5 . Find the probability that the lifetime of a given battery will be (a) less than 6 years, (b) more than 2 years but less than 6 years, and (c) more than 8 years.

a)

To determine

To calculate: The probability that the lifetime of the provided battery would be less than 6 years when it’s lifetime is exponentially distributed with λ=5 by using the exponential probability density function given as,

f(t)=1λet/λ[0,)

Explanation

Given Information:

The lifetime of a battery is exponentially distributed with λ=5.

And the provided exponential probability density function is given as,

f(t)=1λet/λ[0,)

Formula used:

In a probability density function, the probability that x lies in interval [c,d] is given by,

P(cxd)=cdf(x) dx,

Which is shown in the figure below,

Calculation:

Consider the exponential probability density function,

f(t)=1λet/λ[0,)

In order to calculate the probability that lifetime of the provided battery would be less than 6 years integrate f(t) over interval [0,6] with substitution λ=5 in f(t)

b)

To determine

To calculate: The probability that the lifetime of the provided battery would be more than 2 years but less than 6 years when it’s lifetime is exponentially distributed with λ=5 by using the exponential probability density function given as,

f(t)=1λet/λ[0,)

c)

To determine

To calculate: The probability that the lifetime of the provided battery would be more than 8 years when it’s lifetime is exponentially distributed with λ=5 by using the exponential probability density function given as,

f(t)=1λet/λ[0,)

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Evaluate the definite integral. 04x1+2xdx

Single Variable Calculus: Early Transcendentals, Volume I

#### In problems 9-18, simplify the expressions with all exponents positive. 16.

Mathematical Applications for the Management, Life, and Social Sciences

#### If x = ln( sec + tan ), show that sec = cosh x.

Single Variable Calculus: Early Transcendentals

#### Fill in each blank: 10F=C

Elementary Technical Mathematics

#### . ∞ −∞ 1 −1

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 