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.
The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be approximated by a normal distribution, as shown in the figure. (a) What is the minimum UGPA that would still place a student in the top 10% of UGPAs? (b) Between what two values does the middle 50% of the UGPAs lie? 3.4042.8Grade point average μ=3.40 σ=0.17 x A normal curve labeled mu = 3.40 and sigma = 0.17 is over a horizontal x-axis labeled Grade point average from 2.8 to 4 in increments of 0.3 and is centered on 3.40. (a) The minimum UGPA that would still place a student in the top 10% of UGPAs is nothing. (Round to two decimal places as needed.) (b) The middle 50% of UGPAs lies between nothing on the low end and nothing on the high end. (Round to two decimal places as needed.)
Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean ? = 5.6 and standard deviation ? = 0.4. (a) Convert the x interval, 4.5 < x, to a z interval. (Round your answer to two decimal places.) (b) Convert the x interval, x < 4.2, to a z interval. (Round your answer to two decimal places.) (c) Convert the x interval, 4.0 < x < 5.5, to a z interval. (Round your answers to two decimal places.)
The business school at Wassamatta U. receives a large number of applicants to its undergraduate honors program in economics. This photo shows the GPA's of a sample of 260 applicants that have applied to the program in the last several years. From the data the mean GPA is x = 3.13 with standard deviation s = 0.395 1) If a normal model N(3.13,0.395) is an appropriate model for the GPA's of all applicants to the undergraduate honors program in economics, what is the probability that an applicant's GPA is 3.25 or greater? Use three decimal places. 2) what is the actual proportion (a decimal number between 0 and 1) of GPA's in the data that are 3.25 or greater? GPA bins 3.24 2.375 3.63 2.5 3.35 2.625 2.93 2.75 3.26 2.875 3.02 3 3.75 3.125 3.48 3.25 2.77 3.375 2.78 3.5 3.18 3.625 3.58 3.75 2.96 3.875 2.76 4 3.32 3.03 3.18 3.07 3.10 2.88 2.40 3.19 3.16 3.01 2.99…

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