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Get Full Access to Applied Statistics And Probability For Engineers - 6 Edition - Chapter 4.10 - Problem 163e
Get Full Access to Applied Statistics And Probability For Engineers - 6 Edition - Chapter 4.10 - Problem 163e

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# Suppose that the lifetime of a component (in hours) is

ISBN: 9781118539712 55

## Solution for problem 163E Chapter 4.10

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 163E

Problem 163E

Suppose that the lifetime of a component (in hours) is modeled with a Weibull distribution with β = 2 and δ = 4000. Determine the following in parts (a) and (b):

Step-by-Step Solution:

Step 1 of 3

(a)

Suppose that the lifetime of a component ( in hours) is modeled with a Weibull distribution with

We are asked to find the probability

The random variable  with probability density function

is a Weibull random variable with scale parameter  and shape parameter .

The cumulative distribution function of  is

………(1)

We can write  as,

Using equation (1), we can write,

Hence the probability  is

Step 2 of 3

Step 3 of 3

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