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# If T is a continuous random variable that is always ISBN: 9780073401331 38

## Solution for problem 8E Chapter 4.8

Statistics for Engineers and Scientists | 4th Edition

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Problem 8E

If T is a continuous random variable that is always positive (such as a waiting time), with probability density function f(t) and cumulative distribution function F(t), then the hazard function is defined to be the function The hazard function is the rate of failure per unit time, expressed as a proportion of the items that have not failed.

a. If T~ Weibull (α, β), find h (i).

b. For what values of α is the hazard rate increasing with time? For what values of a is it decreasing?

c. If T has an exponential distribution, show that the hazard function is constant.

Step-by-Step Solution:

Step 1:

Let T is a continuous random variable  that is always positive, with probability density function f(t) and cumulative distribution function F(t).The hazard function is the rate of failure per unit time which is defined as

h(t) = Step 2:

We have to find the hazard function h(t), if T~weibull( )

If T~ weibull ( then its pdf will be in the form

f(T)  = , And the cdf of T is

F(T)  =  1-  1-  F(T) =  The hazard function , h(t)  = = = Therefore the hazard function of T is  ,h(t) =  .

Step 3 of 3

##### ISBN: 9780073401331

Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The answer to “If T is a continuous random variable that is always positive (such as a waiting time), with probability density function f(t) and cumulative distribution function F(t), then the hazard function is defined to be the function The hazard function is the rate of failure per unit time, expressed as a proportion of the items that have not failed.a. If T~ Weibull (?, ?), find h (i).________________b. For what values of ? is the hazard rate increasing with time? For what values of a is it decreasing?________________c. If T has an exponential distribution, show that the hazard function is constant.” is broken down into a number of easy to follow steps, and 99 words. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The full step-by-step solution to problem: 8E from chapter: 4.8 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This full solution covers the following key subjects: function, Hazard, rate, values, distribution. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 8E from 4.8 chapter was answered, more than 295 students have viewed the full step-by-step answer.

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