a. Explanation Given info: In a study on “Length of life of a halogen bulb”, the random variable X represent the life (in hours) of a new halogen light bulb and assume that X has an exponential distribution with mean θ = 250 hours. The life distribution of X is considered new better than used ( NBU ) if, P ( X > a + b ) ≥ P ( X > a ) P ( X > b ) . The life distribution of X is considered new worse than used ( NWU ) if, P ( X > a + b ) ≤ P ( X > a ) P ( X > b ) . Calculation: Exponential Distribution: A random variable X is said to follow Exponential distribution if the density function of X is, f ( x ) = 1 θ e − x θ , ( x > 0 , θ > 0 ) . Where the mean is μ = θ and the standard deviation is σ = θ . For exponential distribution, P ( x ≥ a ) = e − a θ . The random variable X follows Exponential distribution with mean θ = 250 hours. For θ = 250 and a = 300 , P ( X > a ) = e − 300 250 = e − 1.2 = 0.3012 . For θ = 250 and b = 200 , P ( X > b ) = e − 200 250 = e − 0.8 = 0.4493 . For θ = 250 and b = 200 a = 300 P ( X > a + b ) = e − ( 300 + 200 ) 250 = e − 2 = 0 b. To determine To show: The exponential distribution is both NBU and NWU when a = 50 and b = 100 . c. To determine To show: For any positive number exponential distribution is both NBU and NWU and explain the reason.

Statistics for Business and Economics (13th Edition)

13th Edition

ISBN: 9780134506593

Author: James T. McClave, P. George Benson, Terry Sincich

Publisher: PEARSON

See similar textbooks

Question

Chapter 4.8, Problem 4.155ACA

To determine

To show: The exponential distribution is both NBU and NWU when a=300 and b=100 .

To determine

To show: The exponential distribution is both NBU and NWU when a=50 and b=100 .

To determine

To show: For any positive number exponential distribution is both NBU and NWU and explain the reason.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.8, Problem 4.154ACA

Chapter 4, Problem 4.156LM

Students have asked these similar questions

The risk of a person developing heart disease is correlated with their BMI (or body mass index), which is calculated by dividing their body mass by their height (high BMIS typically mean the person is overweight). Heart disease is also related to a person's level of activity. Suppose a person's BMI is x and their physical activity is y (measured, for example, in minutes of exercise each day). Let h be a heart disease risk index (high values of h mean high risk of heart disease, low values of h mean a low risk of heart disease). h depends on x and y, that is, h3h(x,y). A simple linear model that only takes into account the effects of BMI and activity is (a) Would you expect a > 0 or a < 0? What about b? You would expect a 7o and b 0. (b) To fit the values of a and b, consider the following data. A patient with BMI of 15, and who does 50 min of activity each day, has risk index h = 150. A patient with BMI of 30, and who does 30 min of activity each day, has risk index h = 405. Use these…

Otitis media is a disease that occurs frequently in the firstfew years of life and is one of the most common reasonsfor physician visits after the routine checkup. A study wasconducted to assess the frequency of otitis media in thegeneral population in the first year of life. Table 4.15 givesthe number of infants of 2500 infants who were first seen atbirth who remained disease-free by the end of the ith monthof life, i = 0, 1, . . . , 12. (Assume no infants have been lostto follow-up.) Disease-free infants ati the end of month i0 25001 24252 23753 23004 21805 20006 18757 17008 15009 130010 125011 122512 1200 Suppose an “otitis-prone family” is defined asone in which at least three siblings of five develop otitis media in the first 6 months of life. What proportionof five-sibling families is otitis prone if we assume thedisease occurs independently for different siblings in afamily?

A regression was run to determine if there is a relationship between the happiness inde expectancy in years of a given country (x). The results of the regression were: ŷ=a+bx a=-1.042 b=0.186

Chapter 4 Solutions

Statistics for Business and Economics (13th Edition)

Ch. 4.1 - Types of random variables. Which of the following...Ch. 4.1 - Types of finance random variables. Security...Ch. 4.1 - NHTSA crash tests. Refer to the National Highway...Ch. 4.1 - Customers in line at a Subway shop. The number of...Ch. 4.1 - Executive pay. Refer to Glassdoor Economic...Ch. 4.1 - Banking. Give an example of a discrete random...Ch. 4.1 - Economics. Give an example of a continuous random...Ch. 4.1 - Hotel management. Give an example of a discrete...Ch. 4.1 - Retailing. Give two examples of discrete random...Ch. 4.1 - Stock market. Give an example of a continuous...

Knowledge Booster

The exponential distribution is both NBU and NWU when a = 300 and b = 100 .

Solution Summary: The author explains that the exponential distribution is both NBU and NWU when a=300 and b=100.

To show: The exponential distribution is both NBU and NWU when a=300 and b=100 .

To show: The exponential distribution is both NBU and NWU when a=50 and b=100 .

To show: For any positive number exponential distribution is both NBU and NWU and explain the reason.

Want to see the full answer?

Chapter 4 Solutions