Let X1, X2, ..., Xn be a random sample from a distribution with a pdf-axae;x > 0f (x) =0, elsewhere.(a) Find the method of moments estimator for a.(b) Find the MLE for a.(c) Find the MLE for the variance of the distribution.

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

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 population has a mean µ = 161 and a standard deviation o = 20. Find the mean and standard deviation of the sampling distribution of sample means with sample size n = 56. The mean is = μx (Round to three decimal places as needed.) and the standard deviation is o- = X 3 X
Use the geometric distribution to derive E(Y), E(Y^2), and V(Y) from the Poisson distribution
Consider the data (1,3), (2,5), (3,9.67) (a) Derive the normal equations for the best fit of the form f(x) = - - + Dx? (b) Find C, D using the normal equations derived above and given data. (c) Find a suitable Linearization for f (x) =- + Dx² (Don't find C, D)
A distribution with µ = 55 and o = 6 is being standardized so that the new mean and standard deviation will be u = 50 and o = 10. When the distribution is standardized, what value will be obtained for a score of X= 58 from the original distribution?
Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.
What is the variance and standard deviation for the number of times the SAT is taken? x Frequency (f) fx f*x2= (f*x) x (x) (4) = (3)x(1) 5152727-(2547473)(2547473)/1518859=880035.3688/1518859=0.5794 (1) (2) (3)=(1)x(2) (4)=(3x1) Population Variance 1 721,769 721,769 721,769 2 601,325 1,202,650 2,405,300 3 166,736 500,208 1,500,624 4 22,299 89,196 356,784 5 6,730 33,650 168,250 Total 1,518,859 2,547,473 5,152,727 880035.3688 0.5794 n=1,518,859 ∑fx = 2,547,473 The population variance is 0.5794 The Standard Deviation? 0.76 Can you show me the steps to reach the standard deviation of .76 ?
Explain at least two differences between the following two point estimations of the population variance. 22 = Σ'1(X, – X)2 n-1 62 _ Σ 1 (X - X)2 =1 = n
The quality characteristic of a product Y consists of three components X1, X2, and X3. The distributions of these components are normal with means 100, 2, 1 and variances 1, 1, 1 respectively. The specifications of the product are 90 ± 8. If Y= X1 + -7X2 + -9X3. Products that are below the lower specification limit are scrapped. Find the proportion of scrapped products = Ф(z).
Let S1^2 be the sampling variance for a random sample of twelve values (amount of mercury in the blood) and let S2^2 be the sampling variance for a random sample of ten values (amount of lead in the blood); samples from the same population were used. The population variance for mercury measurements is assumed to be twice the corresponding population variance for lead measurements. We will further assume that S1^2 is independent of S2^2. 1. Find a number b such that P [(S1^2/S2^2)<=b]=0.95 enter such a b to three decimal places b= 2. Consider the number b calculated above, find a number a such that P[a<=(S1^2/S2^2)<=b]=0.90 enter said a to three decimal places. a=
Vehicle speeds at a certain highway location are believed to have approximately a normal distribution with mean µ = 50 mph and standard deviation σ = 5 mph. The speeds for a randomly selected sample of n = 25 vehicles will be recorded. (a) Give numerical values for the mean and standard deviation of the sampling distribution of possible sample means for randomly selected samples of n = 25 from the population of vehicle speeds. Mean = s.d.(x) = (b) Use the Empirical Rule to find values that fill in the blanks in the following sentence. For a random sample of n = 25 vehicles, there is about a 95% chance that the mean vehicle speed in the sample will be between and mph. (c) Sample speeds for a random sample of 25 vehicles are measured at this location, and the sample mean is 59 mph. Given the answer to part (b), explain whether this result is consistent with the belief that the mean speed at this location is μ = 50 mph. A sample mean of 59 mph (when n = 25) --Select--- be consistent with…
when using delta method to calculate variance, shouldn't [g'(μ)]^2 equal to (θ+1)^4?
Let's draw chance samples with a width of n1 = 10 from a population showing a normal distribution with a mean of 50 and a variance of 64, and a width of n2 = 9 from a population with a mean of 40 and a variance of 81 showing a normal distribution. If X'1 and X'2 show the sample averages, respectively, then what is the probability P |(X'1 - X'2)> 5| ? (X' = X bar)

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

Let X1, X2,..., Xn be a random sample from a distribution with a pdf ax. ae ';x > 0 f(x) 0, elsewhere. (a) Find the method of moments estimator for a. (b) Find the MLE for a. (c) Find the MLE for the variance of the distribution.