MLE: Maximum likelihood estimation (2) Let x1, X2, .. , Xn "ª N(4, 62). Find the MLE of o = (µ, o²), when the parameter spaceis -0 < H < ∞,and o > 0.The following`answers" have been proposed.(a) The MLE of µ and o² are E,Xi, and ÷ E-1x? respectively.(b) The MLE of u and o2 are Xn, and E1(X; – Xn)² respectively.(c) The MLE of µ and o2 are E|Xi, and , E-1(X; – Xn)² respectively.n-(d) The MLE of u and o2 are Xn, and E(X¡ – Xn)² respectively.(e) None of the above.The correct answer is(a)(b)(c)(d)(e)N/A(Select One)

Answered: (2) Let x1, X2 - Xn uª N(4, o2). Find…

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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Constructing a Confidence Interval for a Population Mean If n = 20, ¯xx¯ = 47, and s = 6, construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population.Give your answers to one decimal place. < μμ <
Nicotine Content of Cigarettes A manufacturer of cigarettes wishes to test the claim that the variance of the nicotine content of the cigarettes the company manufactures is equal to 0.616 milligrams. The variance of a random sample of 25 cigarettes is 0.856 milligrams. At α=0.05, test the claim. Assume that the variable is approximately normally distributed. Use the critical value method with tables. (a)State the hypotheses and identify the claim with the correct hypothesis. :H0 ▼(Choose one) :H1 ▼(Choose one) This hypothesis test is a ▼(Choose one) test. b)Find the critical value(s). Round the answers to three decimal places, if necessary. If there is more than one critical value, separate them with commas. Critical value(s)= (c)Compute the test value. Round the answer to three decimal places. χ2= (d)Make the decision. ▼(Choose one) the null hypothesis. (e)Summarize the results. There is…
1) Hypothesis Testing for Population Mean: Population Variance Known a) A restaurant claims that there is an average of 20g of sugar in each slice of their cheesecake. A testing agency purchases 28 slices and finds an average of 22g of sugar per slice. It is known that the sugar content is normally distributed with σ = 5g. Does the sample seem to indicate that the average sugar content in this restaurant's cheesecake is not 20g? Let α = 0.05. Circle the correct null and alternative hypotheses. i) Нo μ = 20 H : μ = 20 Ho μ = 20 Η : μ 20 ii) What is the significance level? iii) Which test statistic will you use? Circle your answer. Ꮓ T x² iv) Calculate the value of the test statistic for the engineer's sample. v) Determine the critical value of the test statistic. Do not round or truncate. vi) Determine the P-value. Do not round or truncate. vii) What is the conclusion? Circle your response. Accept Ho Reject Ho Fail to reject Ho viii) Does the sample seem to indicate that the average…
For a certain knee surgery, a mean recovery time of 11 weeks is typical. With a new style of physical therapy, a researcher claims that the mean recovery time, H, is less than 11 weeks. In a random sample of 92 knee surgery patients who practiced this new physical therapy, the mean recovery time is 10.4 weeks. known to be 2,1 weeks. Assume that the population standard deviation of recovery times Is there enough evidence to support the claim that the mean recovery time of patients who practice the new style of physical therapy is less than 11 weeks? Perform a hypothesis test, using the 0.05 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H,. OSO O=0 (b) Perform a hypothesis test. The test statistic has a normal distribution (so the test is a "Z-test"). Here is some other information to help you with your test. Z00s is the value that cuts off an area of 0.05 in the right tail. • The test statistic has a normal distribution and the value is given by…
Test a claim that the mean amount of lead in the air in U.S. cities is less than 0.038 microgram per cubic meter. It was found that the mean amount of lead in the air for the random sample of 56 U.S. cities is 0.038 microgram per cubic meter and the standard deviation is 0.068 microgram per cubic meter. At alphaαequals=0.01, can the claim be supported? Complete parts (a) through (e) below. Assume the population is normally distributed. d) Decide whether to reject or fail to reject the null hypothesis. ▼ Fail to reject Reject Upper H 0H0 because the standardized test statistic ▼ is is not in the rejection region. (e) Interpret the decision in the context of the original claim. There ▼ is not is enough evidence at the nothing% level of significance to ▼ reject support the claim that the mean amount of lead in the air in U.S. cities is ▼ equal greater than or equal less than or equal not equal greater than less than nothing…
[Statistics] How do you solve this?
Using R, run simulated annealing for a 2 parameter cauchy distribution (with beta constrained to 0.1, so only a single parameter alpha remains) and the negative log-likelihood curve for alpha has serval optima. show a summary graph of the values of alpha visited during the algorithm and how they relate to the position of the optima. data of the cauchy distribution are x<- c(-4.20, -2.85, -2.30, -1.02, 0.70, 0.98, 2.72, 3.50)

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