Assume that n independent count variables {X,,X2,...,X,} are identicallydistributed as X, ~ Poi(0) where i= 1,2,...,n and to estimate E(X,)= 0,consider the sample mean estimator ô = -5x,.n(b)Use the expectation of the distribution of S = nô to compute theexpectation E(@) and the bias of this estimator. State whether thisestimator unbiased.(c)Use the variance of the distribution of S= nô to examine var(Ô) and thestandard error of this estimator.Use the variance and the bias of ê to compute the Mean Squared Error(MSE) of this estimator. Comment on the MSE behaviour in theasymptotic limit as n→o. State whether this estimator is consistent or(d)not.

Answered: Image /qna-images/answer/e43e6ae7-3015-4f06-ac4f-0858d657e45c.jpg

Answered: Assume that n independent count…

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

If we let X1, X2,...X10 be a random sample from the distribution N( μ, σ), then what is the value k so that: P( (X-μ)/(σ/√10) < k ) = .05 P( (X-μ)/(S/√10) < k ) = .05 P( k < (X-μ)/(S/√10) ) = .05
A function has a graph which passes through the point (2,3) and its graph also has the property that the normal line to each point (x,y) on the graph passes through the point (2,0). Find the function?
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
The useful life of a concrete built on the seashore has a Weibull distribution of parameter scale δ> 0 year and power β = 2. Determine a) The half life of concrete EXb) The variance VXc) The probability that the concrete lasts more than 10 years; P (X> 10)
What is the variance of Y_k+1
Let X1, X2, ..., X, be a random sample from f(x;0) = 0e-tI(0,00)(x). Find a 100y or (1- a)100 percent confidence interval for the mean of the population.
Obtain 100 (1 x)% confidence limits (for large samples) for the parameter 2 of the f(x, 2) = e-^.^* ; x ; x = 0, 1, 2,... x! Poisson distribution:
If we assume that the distribution of means is normal, then 95% of all sample means a) will fall in the interval m ± 1.96(σm) b) will fall in the interval m ± 1.645(σm) c) will be no more than 1.645(σm) from μ d) will be no more than from 1.96(σm) from μ
Let X be a random variable with a uniform distribution over the interval [-6,5]. Compute P(X > -0.4) (The answer should be a number rounded to five decimal places, don't use symbols such as % Compute Fx(-2.2). (The answer should be a number rounded to five decimal places, don't use symbols such as
Suppose that X~N(5000,400). You're considering taking a simple random sample and calculating the average of your sample. The Central Limit Theorem tells us that the distribution of all possible sample averages is Normally distributed with a mean of 5000. If you took a sample of size n = 10000, what is the standard deviation of that sample?
A researcher that wanted to estimate the expectation AY of a random variable Y got three independent observations, Y, Y, Y The researcher knows the value o, of the variance of Y and is considering the following estimators: Pi = 4) Yi + (+) ¥ Py = () Yn + (;) ¥½ + () Y½ in (}) Yi + (}) ¥z + (() %D Which of the following is correct? ONone of the above Ois an unbiased estimator of l and it has the smallest variance of the three estimators. Ois an unbiased estimator of µ and it has the smallest variance of the three estimators. O and i, are both unbiased estimators of fl and Var (ſîz) < Var (îì3). is an unbiased estimator of µ and it has the smallest variance of the three estimators.
The average wait time to get seated at a popular restaurant in the city on a Friday night is 12 minutes. Is the mean wait time greater for men who wear a tie? Wait times for 13 randomly selected men who were wearing a tie are shown below. Assume that the distribution of the population is normal. 13, 13, 11, 13, 13, 13, 13, 10, 12, 13, 13, 10, 13 What can be concluded at the the αα = 0.05 level of significance level of significance? The null and alternative hypotheses would be: H0 = (p,u) (<,>,=,not equal) to _____ H1 = (p,u) (<,>,=,not equal) to _____ The test statistic (t,z) = ___ The p-value = _____ Thus, the final conclusion is that ... The data suggest that the population mean wait time for men who wear a tie is not significantly more than 12 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean wait time for men who wear a tie is more than 12. The data suggest the population mean is not significantly more than 12…

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