3. Time intervals (in minutes) X₁,..., Xn between successive eruptions of a geyser are modeledasX₂Exponential (A),where A (> 0) is the eruption rate per minute. We want to report a plausible range for themedian interval time.(d)0Find the MLE of A.(b)(c)Construct an approximate 95% confidence interval for A using the asymptotic distri-bution of AMLE. (Hint: use the approximation method for confidence interval)i.i.d.N=The median of the Exponential(A) distribution, denoted by 8, is a function of A as(log 2)/λ 0.693/A. Calculate an approximate 95% confidence interval for the medianinterval time using the Delta method.Find the Fisher information of A.-

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Answered: 3. Time intervals (in minutes) X₁,...,…

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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(4) Annual rainfall over the slopes of southern Himalayan mountains has varied from 750mm to 1250mm over the last several hundred years. If the distribution of the amount of annual rainfall has mean u = 1000mm and standard deviation o = 100mm, what is the likelihood that the average rainfall over the last ten years could have been below 800mm, in the absence of any climate change? Solve this problem by taking the following four steps one by one. Step (i). We need to compute P(X 10 < 800). where X 10 is the average over the ten years of rainfall. Can we compute this probability exactly: (a) No, the population distribution is not known. (b) Yes, since the population distribution is Poisson. (c) Yes, since the population distribution is Binomial. (d) No, because no matter what the population distribution may be, it is always impossible to find the exact distribution of X 10- (e) None of the above. (a) (b) (c) (d) (e) N/A (i- Select One) Step (ii). An approximation to the probability, P(X…
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#2 A Rollercoaster’s auditors estimate that the average daily loss from those illegally riding without tickets is at least $300, but wants to determine the accuracy of this statistic. The company researcher takes a random sample of losses over 64 days and finds that = $298 and s = $25. a) Test at α = 0.05. Be sure you cover all steps: hypothesis, critical value, acceptance range, conclusion. b) (Unrelated to a’s results) Construct a 95% confidence interval of losses.
2.4
(b) A company produces cylindrical metal rods. The diameters of rods have a normal distribution with mean ucm and variance o' cm?. A random sample of 100 rods is taken and the diameter x, in cm, of each rod is measured. The results are summarised as Ex=52.1 and x = 27.303. (1) Calculate the mean and variance of the population of the diameters of the rods (iii) Detemine a 95% confidence interval for the mean diameter of the rods. (iv) Investigate, at the 1% significance level, whether the mean diameter of the rods is 0.512 cm.
Statistically Graph appropriately with each problem.
7
An article considered regressing y = 28-day standard-cured strength (psi) against x = accelerated strength (psi). Suppose the equation of the true regression line is y = 1900 + 1.3x, and that the standard deviation of the random deviation ϵ is 350 psi. (a) What is the probability that the observed value of 28-day strength will exceed 5000 psi when the value of accelerated strength is 2000? (Round your answer to four decimal places.) (b) What is the probability that the observed value of 28-day strength will exceed 5000 psi when the value of accelerated strength is 2600? (Round your answer to four decimal places.) (c) Consider making two independent observations on 28-day strength, the first for an accelerated strength of 2000 and the second for x = 2600. What is the probability that the second observation will exceed the first by more than 1000 psi? (Round your answer to four decimal places.) (d) Let Y1 and Y2 denote observations on 28-day strength…
N= 150 observations were collected on a time series that was identified as a AR(2) time series. The following statistics were computed from the data. Mean - 45.0 Variance 15.6 Autocorrelation function (up to lag 5) r1 = 0.80, r2 = .50, rз = .26, r4 = -.10, rs = 0.08: == Estimate the parameters of the model using the method of moments.
llMetro by T-Mobile X Group Work-Worksheet#1 on Ch... 1 of 2 Group Work-Worksheet#1 on Chapter 3 0.14% → 1. The Empirical Rule Based on Data Set 1" Body Data" in appendix B, blood platelet counts of women have a normal/bell-shaped distribution with a mean of 255.1 and a standard deviation of 65.4. (All units are 1000 cells/μL.) Using the empirical rule: -30 2.14% 1:40 PM 13.59% 99.73% 95.44% 68.26% 34.13% 34.13% 13.59% 77% 2.14% -20 -10 Mean lo 20 За a. 68.26% of women with platelet counts are within two standard deviations of the mean? The values are from ( b. 95.44% of women with platelet counts are within two standard deviations of the mean? The values are from ( 000 c. 99.73% of women with platelet counts are within two standard deviations of the mean? The values are from ( 0.14%
Need to be done both part's in 30 minutes
You want to obtain a sample to estimate a population mean.you believe the population standard deviations is approximately sigmma=23.3 you would like to be 95% confidence that your estimate is within 1.8 of the true population mean . How large of sample size is required ? The z critical value is given by 1.960

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