Example 18-9. For the distributionBexp {- B (x-p} dx, x 2 Y0, x< YdF =show that for a hypothesis H, that ß = B9, 7 = Yo and an alternative Hị thatB = B1, y= Y1, the best critical region is given by1{nBi - TBo - log k + log iB1- Boprovided that the admissible hypothesis is restricted by the condition Yi S Yo,B1 2 Bo

Answered: Image /qna-images/answer/9c1148d8-779f-4a43-8c14-9ad56eebb9e4.jpg

Answered: mple 18-9. For the distribution dF =…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

A researcher is using a two-tailed hypothesis test with α = 0.01 to evaluate the effect of a treatment. If theboundaries for the critical region are t = ± 2.845, then how many individuals are in the sample?A. n = 23B. n = 22C. n = 21D. n = 20E. cannot be determined from the information given
Consider a study using a between-groups design with between-groups df = 3 and within-groups df = 4. Given an F ratio of 6.8, the researcher should: a. reject the null hypothesis if alpha is .05 but fail to reject if alpha of .01 b. reject the null hypothesis if alpha is .01 but fail to reject if alpha of .05 c. reject the null for both alpha = .01 or alpha = .05 d. fail to reject the null hypothesis whether alpha is .01 or .05
If X1 and X2 constitute a random sample of size n = 2from an exponential population, find the efficiency of 2Y1relative to X, where Y1 is the first order statistic and 2Y1and X are both unbiased estimators of the parameter
Let X1,X2,... be a sequence of identically distributed random variables with E|X1|<∞ and let Yn = n−1max1≤i≤n|Xi|. Show that limnE(Yn) = 0
For a hypothesis test of H0:μ=μ0H0:μ=μ0 against the alternative Ha:μ<μ0Ha:μ<μ0, the z-test statistics is found to be 2.00. This finding is a.significant at neither the 0.01 nor the 0.05 levels. b.significant at the 0.01 level but not at the 0.05 level. c.significant at both the 0.01 and the 0.05 levels. d.not large enough to be considered significant. e.significant at the 0.05 level but not at the 0.01 level.
Let X1...., Xn be a random sample of size n from an infinite population and assume X1 d= a + bU2 with the constants a > 0 and b > 0 unknown and U a standard uniform distributed random variable given by FU (x) := P(U ≤ x) =    0 if x ≤ 0 x if 0 < x < 1 1 if x ≥ 1 1. Compute the cdf of the random variable X1. 2. Compute E(X1) and V ar(X1). 3. Give the method of moments estimators of the unknown parameters a and b. Explain how you construct these estimators!
Consider the following two formulations of the bivariate PRF, where ui and εi are both mean-0 stochastic disturbances (i.e random errors): yi = β0 + β1xi + u yi = α0 + α1(xi − x¯) + ϵ a) Write the OLS estimators of β1 and α1. Are the two estimators the same? b) What is the advantage, if any, of the second model over the first?
Consider the time series xt = β1 + β2t + wt, where β1 and β2 are known constants and wt is a white noise process with variance σ2 w. (a) Determine whether xt is stationary. (b) Show that the process yt = xt − xt−1 is stationary. (c) Show that the mean of the moving average vt = 1 2q + 1 q j=−q xt−j is β1 + β2t, and give a simplified expression for the autocovariance function.
10 Suppose that X is a continuous random variable with pdf given by X(x) =cxα−1e−(x/β)α for x≥0, where α >0,β >0 are some parameters of the distribution, and c is a constant. (a) Find the value of c such that fX is a valid pdf.(b) Find the cdf and the quantile function of X.(c) Ifα= 2 andβ= 4, calculate P(X <1) and find the quartiles of X.
Let X be an exponential random variable with standard deviation σ. FindP(|X − E(X)| > kσ ) for k = 2, 3, 4, and compare the results to the boundsfrom Chebyshev’s inequality.
3.7. Consider the performance function Y = 3x1-2x2 where Xi and X2 are both normally distributed random variables with Ax' = 16.6 0% 2.45 μΧ2 = 18.8 ơx.-2.83 The two variables are correlated, and the covariance is equal to 2.0. Determine the probability of failure if failure is defined as the state when Y 0 3.8. The resistance (or capacity) R of a member is to be modeled using R = R,MPF where Rn is the nominal value of the capacity determined using code procedures and M, P, and Fare random variables that account for various uncertainties in the capacity. If M, P, and F are all lognormal random variables, determine the mean and variance of R in terms of the means and variances of M, P, and F.
Let X1, . . . , Xn, . . . ∼ iid Bern(θ). Consider the Bayes estimator under squared error loss with the Unif(0,1) prior. Show that this estimator is consistent.

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS

mple 18-9. For the distribution dF = {Bexpl-B(x- dl dx, x 2 Y 0, x