2.1Suppose that {x} is a stationary process with constant mean μ₁ = E(x₁) = μ and autocorrelationfunction Pk. Define x = ¹x, to be the sample mean of x₁,x₂,...‚¤‚n 1=1Prove that var(x)=%⁰nQUESTION 2n-11+2-2 (1-4) ₂ Pk where yo = var(x).k=1

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Answered: a stationary process with constant mean…

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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To test Upper H 0H0: muμequals=20 versus Upper H 1H1: muμless than<20, a simple random sample of size nequals=18 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). (a) If x overbarxequals=18.3 and sequals=4.5, compute the test statistic. tequals=nothing (Round to two decimal places as needed.)
9. (8') Let X,, X,, X, be a sample of size n=3 from a distribution with unknown mean u, -0 < u<0, where the variance o is a known positive number. Show that both à =i and ê, = 2X, + X, +5X, are unbiased estimators for H.
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.
A normal distribution has a mean of μμ= 54 and a standard deviation of σσ=6 What is the probability of randomly selecting a score GREATER than 51? A normal distribution has a mean of μμ= 54 and a standard deviation of σσ=6 What is the probability of selecting a sample of n = 4 scores with a mean more than M = 51? A normal distribution has a mean of μμ= 54 and a standard deviation of σσ=6 What is the probability of selecting a sample of n = 36 scores with a mean more than M = 51?
5. S Jn Show that the 95 percent fiducial limits for the mean of the population are x ± to.05, where to.05, stands for the value of t at 5 percent level of significance. Deduce that for a random sample of 16 values with mean 41.5 inches and the sum of the squares of the deviations from the mean 135 (inches)² and drawn from a normal population, 95 percent fiducial limits for the mean of the population are 39.9 and 43-1 inches.
The desired percentage of SiO₂ in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO₂ in a sample is normally distributed with = 0.32 and that x = 5.23. (Use a = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses. O Ho: μ = 5.5 H₂:μ> 5.5 O Ho: μ = 5.5 H₂: μ = 5.5 ⒸHO: μ = 5.5 H₂:μ ≥ 5.5 O Ho: μ = 5.5 H₂: μ< 5.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z = P-value = State the conclusion in the problem context. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true verage percentage differs from the desired percentage. O Reject the null hypothesis. There is not sufficient evidence to…
let Y=5X+10 and X be normally distributed with a mean 10 and varience 25. find P(Y<54).
4
Estimate ff e+y“ dA with R = [0, 3] × [0, 3] using m = n = 2 and midpoints as your R sample points.
A random sample of 41 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.09 years, with sample standard deviation s = 0.83 years. However, it is thought that the overall population mean age of coyotes is μ = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use α = 0.01. Solve the problem using the critical region method of testing (i.e., traditional method). (Round your answers to three decimal places.) test statitics= critical=
Vehicle speeds at a certain highway location are believed to have approximately a normal distribution with mean µ = 50 mph and standard deviation σ = 5 mph. The speeds for a randomly selected sample of n = 25 vehicles will be recorded. (a) Give numerical values for the mean and standard deviation of the sampling distribution of possible sample means for randomly selected samples of n = 25 from the population of vehicle speeds. Mean = s.d.(x) = (b) Use the Empirical Rule to find values that fill in the blanks in the following sentence. For a random sample of n = 25 vehicles, there is about a 95% chance that the mean vehicle speed in the sample will be between and mph. (c) Sample speeds for a random sample of 25 vehicles are measured at this location, and the sample mean is 59 mph. Given the answer to part (b), explain whether this result is consistent with the belief that the mean speed at this location is μ = 50 mph. A sample mean of 59 mph (when n = 25) --Select--- be consistent with…
Solve with R, please

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a stationary process with constant mean μ, = E(x₁) = μ and auto ==x, to be the sample mean of x₁, X2 ..., Xµµ n =l k r(x)=. Yo x) = ² = [1 + 2 Σ (1-4) 0₂ ] n k=1 Pk where % = var(x,).