   Chapter 9.3, Problem 43E ### 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
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# Useful Life The time t (in years) until failure of an appliance is exponentially distributed with a mean of 2 years.(a) Find the probability density function for the random variable t.(b) Find the probability that the appliance will fail in less than 1 year.

(a)

To determine

To calculate: The probability density function for the random variable t, if the time t (in years) until failure of an appliance is exponentially distributed with a mean of 2 years.

Explanation

Given information:

The time t (in years) until failure of an appliance is exponentially distributed with a mean of 2 years.

Formula used:

The exponential probability density function,

f(x)=aeax  , 0x<

Here, an expected value is,

μ=1a

Calculation:

The provided time is t,

Consider a function as f with respect to t, and the time t (in years) until failure of an appliance,

Use the formula of the exponential probability density function, the function will be,

f(t)=aeat

To find the value of a use the formula

(b)

To determine

To calculate: The probability that the appliance fails in less than one year, if the time t (in years) until failure of an appliance is exponentially distributed with a mean of 2 years.

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