An electrical component has a time to failure (or lifetime) distribution that is exponential with parameter lambda , so the mean lifetime is mu 1 lambda Suppose that a sample of n of these components is put on test, and let Xi be the observed lifetime of component i The test continues only until the rth unit fails, where r We have previously shown in Exercise 7 72 that Tr r is an unbiased estimator for mu (a) It can be shown that 2 lambda Tr has a chi square distribution with 2r degrees of freedom Use this fact to develop a 100(1 a) confidence interval for mean lifetime mu 1 lambda (b) Suppose 20 units were put on test, and the test terminated after 10 failures occurred The failure times (in hours) are 15, 18, 19, 20, 21, 21, 22, 27, 28, 29 Find a 95 confidence interval on mean lifetime T, E x, (n r) X, 3D

Question: An electrical component has a time-to-failure (or lifetime) distribution that is exponential with parameter λ, so the mean lifetime is μ = 1/λ. Suppose that

An electrical component has a time-to-failure (or lifetime) that is exponential with parameter λ, so the mean lifetime is μ = 1/λ. Suppose that a sample of n of these components is put on test, and let Xi be the observed lifetime of component i. The test continues only until the rth unit fails, where r

We have previously shown in Exercise 7-72 that Tr/r is an unbiased estimator for μ.
(a) It can be shown that 2λTr has a chi-square with 2r degrees of freedom. Use this fact to develop a 100(1 €“ a) % confidence interval for mean lifetime μ = 1/λ.
(b) Suppose 20 units were put on test, and the test terminated after 10 failures occurred. The failure times (in hours) are 15, 18, 19, 20, 21, 21, 22, 27, 28, 29. Find a 95% confidence interval on mean lifetime.

T, = E x, + (n - r).X, %3D

Step by Step Solution

★★★★★

3.47 Rating (170 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a PX3 2T X1 P 21 21 Then a confidence ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

M-S-S-S-I (86).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

The time to failure of an electrical component has a Weibull distribution with parameters = 0.056 and a = 2.5. A random collection of 500 components is obtained. Estimate the probability that at...

The resistance X of an electrical component has a probability density function f (x) = Ax (130 -x2) for resistance values in the range 10 x 11. (a) Calculate the value of the constant A. (b)...

Suppose a random sample of n measurements is selected from a population with mean = 100 and variance 2 = 100. For each of the following values of n, give the mean and standard deviation of the...

An electrical component has a time-to-failure (or lifetime) distribution that is exponential with param- eter , so the mean lifetime is = 1/A. Suppose that a sample of n of these components is put on...

LAB ACTIVITY #3 For each part of this lab, SUBMIT your solution to everything asked in BOLD RED in Problems 1-6 below. Include the respective R code and output. Part 1 (Continuous Distributions in R)...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

I need help with this study guide I'm making Flashcards from these Questions, I've Bolded the ones I think are right please correct me if I'm wrong. 1. What is the best interpretation for the...

solve these problems The difference between the number of customers in line at the express checkout and the number in line at the superexpress checkout in Exercise 3 is X, - X2 Calculate the expected...

Have you ever wondered why people act the way they do on Black Friday or on the 4th of July? Or why wealthy people and nations have less children than poorer ones? Or why we buy flowers or a card for...

file: simulate_python2.py from mpl_toolkits.mplot3d import Axes3D import matplotlib.pyplot as plt import numpy as np import random import sys def plot_gaussian(x,y,z,filename=None): """ Plot the...

Define like-kind property as it applies to like-kind exchanges, and give examples of like-kind properties and properties that are not of like-kind.

Which of the following is the characteristic of the particle of the matter? Options: 1) Particles of matter repel each other 2) Particles of matter attract each other 3) Particles of matter neither...

A . Do you agree with the president that revision of the $ 3 . 7 0 standard cost figure is not necessary? List your references list that you use in your analysis.B . Assume that you conclude that the...

What would an upward-sloping demand curve imply about the marginal utility derived from consumption? Why aren't upward sloping demand curves observed in the real world?

The shareholders equity section of Pioneer Enterprises as of December 31, 2015, follows: Common stock (10,000 shares issued @ $6 par) ...... $ 60,000 Additional paid-in capital (C/S)...

Ski n Cycle purchased Elan 200 skis for $492 per pair and priced them to give a 40% rate of markup on selling price. When this model was discontinued, the store marked down its remaining stock by...

The exchange rate between the US$ and the C$ declines from US$0.8993 to US$0.8846 per C$. What will be the change in the C$ price to an importer of a US$2000 item?

Rory invested a total of $7800 in shares of ABC Ltd. and XYZ Inc. One year later the investment was worth $9310, after the shares of ABC had increased in value by 15% and the shares of XYZ were up...

Reduce the equation to one of the standard forms, classify the surface, and sketch it. x 2 = 2y 2 + 3z 2

Refer back to the previous exercise. Recall that the data file TVLife provides information on life expectancy and number of televisions per thousand people in a sample of 22 countries, as reported by...

Which of the following does the method of least squares minimize? A. Sum of vertical distances between observations and the line B. Sum of squared vertical distances between observations and the line...

Explain what is wrong with the following statements about correlation and regression. a. The correlation between the number of years of education and yearly income is 1.23. b. The regression equation...

Greater risk reduction can be achieved when security returns are A . high B . negatively correlated C . positively correlated D . uncorrelated

1.The GMAT is approximately normally distributes with a mean of 527 and a standard deviation of 112. What is the probability of an individual scoring above 500 on the GMAT? 2.How high must an...

If Smolinski, Incorporated, were an all-equity company, it would have a beta of 1.05. The company has a target debt-equity ratio of .40. The expected return on the market portfolio is 10 percent and...