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10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 9, Problem 58RE

Textbook Problem

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**Useful Life** The time *t* (in hours) until failure of a mechanical unit is exponentially distributed with a mean of 350 hours.

(a) Find the probability density function for the random variable *t.*

(b) Find the probability that the mechanical unit will fail in more than 400 hours but less than 500 hours.

**(a)**

To determine

**To calculate:** The probability density function for the random variable *t* (in hours) until the failure of a mechanical unit which is exponentially distributed with a mean of

**Given Information:**

The time taken (in hours) until failure of a mechanical unit is exponentially distributed with a mean of

**Formula used:**

The probability density function exponential distribution for

Here,

**Calculation:**

Consider the provided information of failure time of a mechanical unit.

As *a* is calculated as,

Use the definition of exponential probability density function

**(b)**

To determine

**To calculate:** The probability that the mechanical unit will fail in more than *t* (in hours) until the failure of a mechanical unit which is exponentially distributed with a mean of

Calculus: An Applied Approach (MindTap Course List)

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