   Chapter 9.2, Problem 36E ### 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 time t (in years) until failure of a component in a machine is exponentially distributed with λ   =   3.5 . Find the probability that the lifetime of a given component will be (a) less than 1 year, (b) more than 2 years but less than 4 years, and (c) at least 5 years.

a)

To determine

To calculate: The probability that the lifetime of the provided component would be less than 1 year when the time t until failure of a component in a machine is exponentially distributed with λ=3.5 by using the exponential probability density function given as,

f(t)=1λet/λ[0,)

Explanation

Given Information:

The time t until failure of a component in a machine is exponentially distributed with λ=3.5

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 [0,1] with substitution λ=3.5 in f(t).

Thus,

P(0<t<1)=0113

b)

To determine

To calculate: The probability that the lifetime of the provided component would be more than 2 years but less than 4 year when the time t until failure of a component in a machine is exponentially distributed with λ=3.5 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 component would be at-least 5 years when the time t until failure of a component in a machine is exponentially distributed with λ=3.5 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

#### In Exercises 1-6, simplify the expression. 5. (4x1)(3)(3x+1)(4)(4x1)2

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In Problems 35-42, simplify each complex fraction. 42.

Mathematical Applications for the Management, Life, and Social Sciences

#### Finding a Limit In Exercises 1128, find the limit. limx6(x2)2

Calculus: Early Transcendental Functions (MindTap Course List)

#### For

Study Guide for Stewart's Multivariable Calculus, 8th 