b)Let X₁, X2,..., Xn be a random sample with the following probability density functioni)ii)iii)f(x) =If n = 7, use the fact thatsize a = 0.01.хе вBB20XShow that the best critical region for testing Ho : B = 4 against H₁: B=8 is £x; ≥C.i=1nSENTX>0, elsewhereX; is xan toX4netermine the best critical region ofBased on the critical value in (ii), compute the power of the test.

Answered: Image /qna-images/answer/6be37b1a-f239-45d9-8326-bd4e9ad2b6f0.jpg

Answered: b) Let X₁, X2,..., Xn be a random…

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

Suppose X,,X,,...,X, is a random samples from normal distribution with mean, µand variance, n ΣΧ Let Y,, Y2,., Y, be an independent chi square distribution, each with 1 i=1 1 and X= degree of freedom. State the distribution and parameter(s) of each of the following random variables. a) J= \n(X – u)
Let Y1, Y2,..., Y, denote a random sample from the density function given by 1 yª-'e=y/®, y> 0, f(y[a, 0) = elsewhere, where a > 0 is known. a Find the MLE Ô of 0. b Find the expected value and variance of ê. c. Is the MLE ô an unbiased estimator for 0?
has a 10 chtance of tontainlig a srgame pollutant. Assume that the suuples are andependent Mith regard to the presence of the pollutant. Find the probalility that the next 18 saples (i) exactly 3 contain the pollntant. (ii) at least two samples containm the pollutint. The time takes to repair a particular machine in a factory is a random variable with density function fr(1) = 0. elsewhere fa) Find a. (b) Find the Eumulative distributjon metion and use it to caleulate P(0 < X < I).
b) Let X to be a random sample from a distribution with a probability density function given by f(x; 0) = {0x0-¹,if 0 i) Find the level of significance of the test, a. ii) Calculate the power of the test.
Let X1,..., X10 be a random sample of size 10 from a N(u, o²) population. Suppose 10 Y =(X; - 4)? i=1 Find the probability that the random interval Y Y 20.5' 3.25 includes the point o?.
2.70 Let X and Y be random variables with joint density function (4xy, 0< x,y< 1, f(x,y)= {0, elsewhere. Find the expected value of Z = √X² + y².
3. If the probability density function of random variable is given by f(x)=1/sechx 1 ≤ x ≤ 2 a) Find the mean b) Find the total area
Let X; (i = 1, 2,..., n) be i.i.d. exponential random variables with E{X;} = 1/A. Let Y = mn{X1, X2,..., Xn}. What is the distribution of Y? (Compute P{Y > y}.) What is the distribution of Z = max{X1, X2, ..., Xn}? (Compute P{Z < z}.)
7. The random vector (X, Y)T follow a bivariate normal distribution: 025)). Let D(z) denote the cdf of N(0,1), i.e., (z) = P(Z ≤ z) = exp(-)du, whereZ~ N(0,1). If a. b. C. d. e. What is the marginal distribution of X? Please express P(1
Let X1, . . . , Xn be independent random variables, such that Xi ∼ Poiss(λi), for i = 1, . . . , n. Find the distribution of Y = X1 + · · · + Xn.
5. Let X be a random variable with a uniform distribution on the interval (0,1). Given Y = e, derive a) b) the probability distribution function of Y = e*. the probability density function of Y.
Let Z₁ = X₁-μx ~N(0,1), and Wi σχ = Yi-HY~N(0,1), for i = 1,2,3,...,10, then: oy i) State, with parameter(s), the probability distribution of the statistic, T = ii) Find the mean and variance of the statistic T = Σt, wi? Σ, Z² Σt=1Zi 4i=1 iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4. iv) Find the value of such that P(T > B) = 0.01, where T = Σ₁₁Z₁² + 10₁ W₁². ẞ Σ{1Z2 Σi,

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