Suppose that a sequence of mutually independent and identically distributed discrete randomvariables X₁, X₂, X3,..., X, has the following probability density functiona)b)c)d)e)f(x; 0) =Show that for any e > 0 and SnE=72exe-0x!0,Jfor x = 0,1,2,...elsewhere1 Xi, lim P(IS-01 ≥ 8) = 0.11-00Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 8.Let ₁ = X1+2X2+2X3-X4¹ and ₂ = (X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Whichone of the two estimators is more efficient?What is the Cramer-Rao lower bound for the variance of the unbiased estimator of theparameter 8?Use the one-parameter regular exponential family definition to find the functions,h(x), c(0), w (0) and t(x). Suppose that a sequence of mutually independent and identically distributed discrete randomvariables X₁, X₂, X3,..., X, has the following probability density functiona)b)c)d)e)f(x; 0) =Show that for any e > 0 and Sn=720xe-0x!0,Jfor x = 0,1,2,...elsewhere1 Xi, lim P(IS-01 ≥ 8) = 0.11-00Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 8.Let ₁ = X1+2X2+2X3-X4¹ and ₂ = (X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Whichone of the two estimators is more efficient?What is the Cramer-Rao lower bound for the variance of the unbiased estimator of theparameter 8?Use the one-parameter regular exponential family definition to find the functions,h(x), c(0), w (0) and t(x).

As per bartleby guidelines we can solve only first three subparts and rest can be reposted

Answered: Show that for any & > 0 and Sn = Ei=1…

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 that X and Y are independent random variables each with a x²(4) distribution. Find the moment generating function of U = X +5Y and evaluate the expectation value E(U). State clearly and justify all steps taken. Hint: You may use without proof the fact that the moment generating function of a x²(v) random variable W is Mur-(t) = (-)". 2t
IT HAS BEEN FOUND THAT A FLUCTUATING ELECTRIC CURRENT X AT ONE OF THE ESKOM SUBSTATIONS HAS A UNIFORM PROBABILITY DISTRIBUTION, f(x) = a≤x≤b otherwise a+b (b-a)² WITH E(X) = AND Var (X) = 12 AS THE STATISTICIAN AT ESKOM AND HAVE BEEN GIVEN A RANDOM SAMPLE OF 7 MEASUREMENTS X₁, X₂,,X, OF THE ELECTRIC CURRENT TO INFER ABOUT THE MEAN FLUCTUATION OVER A SPECIFIC PERIOD. AFTER CAREFUL CONSIDERATION YOU HAVE IDENTIFIED THREE POSSIBLE ESTIMATORS 0₁ = X₁+X7, 0₂ = X₁ +2X₂+X AND 3 = X 3 Show which of the estimators possess this property
1a) Derive a maximum-liklihood estimator for the unknown parameter Y 1b) An experienced sales person completes sales following a Poisson distribution, with a mean rate of Y = 1.8 sales/month. A junior sales person completes sales at a mean rate of Y = 0.85 sales per month Find the probability of the joint sales team (experienced and junior) completing exactly 2 sales in any given months, assuming the two sales people act independently of each other. 1c) Find the probability of the joint sales team (experienced and junior) completing more than 2 sales in any given months
Consider a random sample X1,...,Xn,... ∼ iid Beta(θ,1) for n > 2. Prove that the MLE and UMVUE are both consistent estimators for θI got MLE = n/-∑logXi and UMVUE = (n-1)/∑logXi. Need help in proving consistency
2) Let X₁, X2, X3, X4 be a random sample of size 4 from a population with the following distribution function Where, ß > 0. If fram e ¹- {** f(x;0)=B for x > 4 otherwise "1 g) What is the maximum likelihood estimator of g (B) = 2(ß + 1). h) Is the maximum likelihood estimator of g (B) = 2(B + 1) unbiased or not?
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
2 If X₁ and X₂ are the means of independent ran- dom samples of sizes n₁ and n₂ from a normal population with the mean u and the variance o2, show that the vari- ance of the unbiased estimator 2 w X₁ + (1-w). X₂ is a minimum when @ = n1 n₁ + n₂ idnu
Let X1, X2,...X, be a random sample from f(x,e) = -.0 < x< 8, then T= max(X,} is a %3D complete statistic for the parameter 0 Select one: O True False
please include all the steps. thank you
Two random variables X and Y have joint char- acteristic function l@,,m)=exp(-20,?-80;) (i) Show that X and Y are zero mean ran- dom variables.
If the roots of the quadratic equation x – ax + b = 0 are real and b is positive but otherwise unknown, what are the expected values of the roots of the equation. Assume that b has a uniform distribution in the permissible range. -
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

Show that for any & > 0 and Sn = Ei=1 Xi, lim P(|Sn-01 ≥ E) = 0. 11-00 a) b) Show that a statistic S, in a) is the maximum likelihood estimator of the parameter 8. Let 0₁ = X₁+2X2+2X₁-X and ₂ = (X₁ + X₂ + X₂ + X₁) be two unbiased estimators of 8. Which