7. For the example dealing with the accelerated life testing discussed in the lectures, thereare 25 uncensored observations at 70°C that are assumed to be observations onindependent Exponential random variables with mean 070. The maximum likelihoodestimate of 070 is Ô70 = 97.44. The relative likelihood function evaluated at 070 = 90 isclosest toA)0.922B) 0.3C)0.919D) 0.718

No. of uncensored observations at , These are on independent exponential random variables with mean…

Answered: 7. For the example dealing with the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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You have determined that in the past three years there 7 of the 14 were hand injuries. Previous projections had indicated that under normal conditions, only four hand injuries were expected and 12 other injuries were expected. The remaining injuries were due to other causes. Calculate the chi-square value and discuss whether there was a significant difference in observed data vs. the expected data. Also discuss how the process of hypothesis testing might prove helpful o = 7 hand injuries and 7 other injuriese = 4 expected hand injuries and 12 other injuries
When we consider a random sample of size n as X,..., X, which is from Binomial (n, 6). X+1 a. Is a biased estimator for the parameter 8? Is this estimator asymptotically unbiased? n+1 b. Find the mean squared error (MSE) of the estimator. Investigate its MSE consistency.
The third worksheet labeled sample B is a simple random sample with replacement, with seven observations in the sample, from some population. The index i in the first column is just an integer name for each observation. The specific values x in the second column are measures of a random variable X distributed in the population. Now suppose this random variable X is known to have a Normal distribution in the sampled population. You still do not know the population mean and must estimate it from the sample, as you did earlier. BUT NOW, in this question, you know in advance that the true population standard deviation of the random variable X is 4. Compute the standard error (of the sample mean), given this new knowledge situation. i xi 1 74.2 2 72.79 3 70.35 4 74.37 5 73.34 6 78.96 7 77.99
The lifetime of an electronical component is to be determined; it is assumed that it is an ex- ponentially distributed random variable. Randomly, users are asked for feedback for when the component had to be replaced; below you can find a sample of 5 such answers (in months): 19,23,21,22,24. Fill in the blanks below. (a) Using the method of maximum likelyhood, the parameter of this distribution is estimated to 2 = WRITE YOUR ANSWER WITH THREE DECIMAL PLACES in the form N.xxx. DO NOT ROUND. (b) Let L be the estimator for the parameter of this distribution obtained by the method of moments (above), and let H be the estimator for the parameter of this distribution obtained by the method of maximum likelyhood. What comparison relation do we have between L and M in this situation? Use one of the symbols to fill in the blank. L M
part 4b
None
The third worksheet labeled sample B is a simple random sample with replacement, with seven observations in the sample, from some population. The index i in the first column is just an integer name for each observation. The specific values x in the second column are measures of a random variable X distributed in the population. Now suppose this random variable X is known to have a Normal distribution in the sampled population, BUT you do not know the population mean or the population standard deviation of that Normal distribution: Both must be estimated from the sample as you just did. Compute the lower bound of an 80% confidence interval for the population mean, using the appropriate sample estimates and techniques appropriate to the knowledge situation described above. i xi 1 74.2 2 72.79 3 70.35 4 74.37 5 73.34 6 78.96 7 77.99
Suppose that a random sample X₁, X2, X20 follows an exponential distribution with parameter B. Check whether or not a pivotal quantity exixts, if it exists, find a 100(1 - α)% confidence interval for B. www.
question 12.12 using the numbers from 12.11.
Only 3 and 4part
e 14-25. A car hire firm has two cars which it hires out day by day. The number of demands for a car on each day is distributed as a Poisson variate with mean 1-5. Calculate the proportion of days on which (i) Neither car is used (ii) Some demand is refused.
A random sample of size n = 28 is obtained from a normally distributed population with a population mean of u = 350 and a variance of o =145. a. What is the probability that xr < 345? b. What is the probability that the sample variance is less than 140? c. What is the probability that the sample variance is greater than 175?

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