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

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?

1. In an epidemic, the probability of having S|D is 0.2 and P(D) = 0.1. P(S|D') = 0.04 and P (D') = 0.01. What is the P(D|S)? 2. The relationship between weight and age was found to have a linear relationship, with expression weight= 3.0 (age) +10. Predict the weight of a girl whose age is 20 years? 3. A. If a z score of 1.95 is equal to a p of 0.9744, what proportion is greater than1.95 B. From question A, what proportion is between the mean and 1.95? 4. If a the constant for a regression is 0.8 and the standard deviation for the x variables is 4 while the standard deviation for the y variables is 6. What is the correlation coefficient r? 5. In a class of 20 students, twelve take mathematics and genetics, while eight take genetics only. What is the probability of selecting a student who takes only mathematics?

Environmental conditions can affect the growth of coral. To study this, a researcher examined a species of coral that is found in the Caribbean Sea and the Gulf of Mexico. At 12 localities, he determined the average annual calcification rate of coral over a period of several years and the average annual maximum sea surface temperature during the same period. Calcification rate affects the growth of coral, with higher rates corresponding to greater growth. The table contains data for these 12 localities. Maximum sea surface temperature (°C) and calcification rate (g cm² yr¯¹) Maximum Sea Surface Temperature 29.4 29.4 29.4 29.6 29.1 28.7 Calcification Rate 1.48 1.53 1.52 1.48 1.31 1.25 Maximum Sea Surface Temperature 29.7 29.5 29.4 29.0 29.0 29.0 Calcification Rate 1.63 1.53 1.46 1.24 1.29 1.12 To access the complete data set, click the link for your preferred software format: Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt! The residuals for average annual maximum sea surface…

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