2.2.Let Y1, Y2, ..., Yn denote independent and identically distributed random variables from apower family distribution with parameters a and 0 = 3. Then, as in Exercise 9.43, if a > 0,[ay-/3".0 sys 3,f0=0,elsewhere.Show that E(Y,) = 3a/(a + 1) and derive the method-of-moments estimator for a.Also determine if the estimator is unbiased for a.

Answered: Image /qna-images/answer/98995c88-7633-4b22-a11d-717870ff6e60.jpg

Answered: 2.2. Let Y1, Y2, ..., Y, denote…

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

Let a stochastic process (Xt) be given as follows: Xt = 3 + 0:5Xt-1 + t, where (t) is white noise with var ( t) = 1. a) What process is (Xt)? b) Explain briefly why this is a \conditional expectation" model, but not a \conditional variance" model. c) Suppose we observed Xt = 2:5, Xt-1 = 1:7. Compute a forecast for Xt+1. d) Suppose we observed Xt = 2:5, Xt-1 = 1:7. Compute a forecast for the variance of the process at time t + 1, that is, for the variance of Xt+1.
Suppose that Y₁, Y₂, ..., Ym is a random sample of size m from Gamma (a = 3, B = 0), where 0 is not known. Check whether or not the maximum likelihood estimator Ô is a minimum variance unbiased estimator of the parameter 8.
5. Suppose Y₁, Y2,..., Y are independent random variables whose density is for y0 for some > 0. (a) Show that the MLE for is f(y) = 30y²e-04³ n ÔMLE = ΣΤ (b) Use the R code to estimate the bias and the variance when n = 20 and 0 = 2.
"" please answer alll
Suppose Y₁,..., Yn are independent random variables each with the Pareto distribution and E(Y) = (Bo + B1Xi) Is this a generalized linear model with a canonical link? Give reasons for your answer.
a) Let X₁, X₂, X3,..., X, be a random sample of size n from population X. Suppose that X~N(0, 1) you and Y = -√n. VR i) Show that the standard score of the sample mean X, is equal to Y. ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively. iii) Show using the moment generating function technique that Y is a standard normal rando... variable. iv) What is the probability that Y² is between 0.02 and 5.02? b) Let X₁, X₂, X, and Y₁, Y₂.... Y be random samples from populations with moment generating functions Mx, (t) = eat+t² and My (t) = (-), respectively. 25 i) Find the sampling distribution of the statistic W = X₁ + 2X₂ X3 + X₁ + X5. ii) What is the value of the sample size n, if PIX(X-X)2> 68.3392] = 0.025? iii) What is the value of the sample size m, if P(|Y-Hy ≥10) <0.04? QUESTION A
2
Suppose you have a random sample of observations from random variables Xi, i=1, 2, .., n. Assume that X;'s are identically distributed and they have the following distribution function: f(x;;0) =o* (1–ơ), x; = 1,2 , 3., 0
Show that two random variables X, and X, with joint pdf. Sx, x, (*1 »*2) = 16 Xl< 4, 2< X2<4 are independent and orthogonal.
Exercise 3: Find MVUE for 0, in each of the following cases: 1. (X1, X2, ... ,Xx,} is a random sample from Gamma(4,0). 2. (X1, X2, ... ,X,} is a random sample from Binomial (10, 0). 3. (X1, X2, ...,Xx,} is a random sample from Poisson(0).
a) Let X₁, X₂, X₁,...,X, be a random sample of size n from population X. Suppose that X-N(0, 1) and Y = -1-8√n. i) Show that the standard score of the sample mean X, is equal to Y. ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively. iii) Show using the moment generating function technique that Y is a standard normal random variable. iv) What is the probability that Y2 is between 0.02 and 5.02?
Suppose that X₁ = 1; X₂ = 1; X3 = 0; X₁ = 1; X5 = 1, X6 = 1; X₂ = 0; X = 1; X9 = 0, X10 = 0, represents a random sample. Each of these X's comes from the same population and has a density of fx₁ = 0¹-* (1 - 0)*; x = 0,1 First determine the form of the maximum likelihood estimator for 0, then use the MLE formula and the data provided to find an estimate for 0. Round your answer to 3 decimal places. (Answer is 0.4)

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

2.2. Let Y1, Y2, ..., Y, denote independent and identically distributed random variables from a power family distribution with parameters a and 0 = 3. Then, as in Exercise 9.43, if a > 0, J ay-/3", 0