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Chapter 5: Q. 5.23 (page 216)

Compute the hazard rate function of a Weibull random variable and show it is increasing when 𝛽≥1and decreasing when 𝛽≤1

Short Answer

Expert verified

The hazard rate function of Weibul distribution is H(t)=𝜆t𝛽

Step by step solution

01

Given Information

X is a Weibull distribution with parameters 𝛌,𝛂and𝞫

02

Calculations

The hazard function of Weibull function is

H(t)=𝜆t𝛽

03

Plot

In order to better understand we need to see the graph of above function that is

where green graph is for the case when 𝛽≤1and black graph is for the case when localid="1650453593374" 𝛽>0.

This proves the statement thathazard rate function of a Weibull random variable and show it is increasing whenand decreasing when

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Most popular questions from this chapter

A randomly chosen IQtest taker obtains a score that is approximately a normal random variable with mean 100and standard deviation 15. What is the probability that the score of such a person is

(a) more than 125;

(b) between 90and 110?

Show that Zis a standard normal random variable; then, for,x>0

  1. P{Z>x}=P{Z<−x}
  2. P{|Z|>x}=2P{Z>x}
  3. P{|Z|<x}=2P{Z<x}−1

Let X be a normal random variable with mean 12and variance 4. Find the value of csuch that localid="1646649699736" PX>c=0.10.

If Xis a normal random variable with parameters μ=10and σ2=36, compute

(a)role="math" localid="1646719347104" PX>5

(b)role="math" localid="1646719357568" P4<X<16

(c)role="math" localid="1646719367217" PX<8

(d)PX<20

(e)PX>16

A filling station is supplied with gasoline once a week. If its weekly volume of sales in thousands of gallons is a random variable with probability density function

f(x)=5(1−x)40<x<10otherwise

what must the capacity of the tank be so that the probability of the supply being exhausted in a given week is role="math" localid="1646634562935" .01?
See all solutions

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