   Chapter 9.3, Problem 39E ### 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

# Useful Life The useful lifetime of a product is modeled by the probability density function f ( t ) =   0.4 e − 0.4 t where t is the time (in years), with 0   ≤ t <   ∞ . Find the mean and median useful lifetimes.

To determine

To calculate: The mean and median of the useful life time of a product modelled by the probability density f(t)=0.4e0.4t function.

Explanation

Given information:

The useful lifetime of a product modelled by the probability density function f(t)=0.4e0.4t where ‘t’ is the time in years with 0t.

Formula used:

If ‘f’ is the probability density function of a continuous random variable x over the interval [a,b], then the expected value or mean is given by;

μ=E(x)=abxf(x)dx

And, the median ‘x’ is the number m such that;

amf(x)dx=0.5

The formula for integration by parts is;

uvdx=uvdxdudx[vdx]dx

Calculation:

Consider given probability density function

f(t)=0.4e0.4t;0t

Consider the primary equation

μ=E(t)=0tf(t)dt=0t×0.4e0..4tdt=0.40te0.4tdt

Solve by integration by parts uvdx=uvdxdudx[vdx]dx as here u=x and v=e0.4t therefore;

μ=0.40te0.4tdt=0.4[te0

### 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 516, evaluate the given quantity. log4116

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Evaluate the integral, if it exists. 01(u4+1)2du

Single Variable Calculus: Early Transcendentals, Volume I

#### Which graph represents y=x+1x

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

#### What is the goal of a single-case experimental research design?

Research Methods for the Behavioral Sciences (MindTap Course List) 