7.38 Let X have the negative binomial distributionx-f(x) =(1) p²(1-P) X-Pp' (1-p) for x=r₁r+1, ...(b)(a) Obtain the maximum likelihood estimator of p.For one engineering application, it is best to usecomponents with a superior finish. Suppose X =27 identical components are inspected, one at atime, before the r = 3rd component with superiorfinish is found. Find the maximum likelihood esti-mate of the probability that a component will havea superior finish.

Answered: Image /qna-images/answer/72b4e159-584e-44c7-a55a-2aa0f220051b.jpg

Answered: 8 Let X have the negative binomial…

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

12. Suppose (1, 2, ..., n) is a random sample from ...,n) is a random sample from a normal distribution, find the absolute efficiency of the maximum likelihood estimator of 0 if, x; ~ ~ N(0, 1).
(e) Show that the sample mean of a simple random sample (drawn without replacement from a normal population) is dis- tributed normally with mean u and variance -² (1--=-1). n where N and n are population and sample sizes respectively. 4 In the 1 1 TI
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?
If X is distributed as normal with μ = 20 and σ2 = 40 and a random sample of 16 variates is drawn from the population, what is the probability that their sample mean will be between 17 and 2?
18. Show that for type lII population - x/0 dp O
A random sample of 10 observations from population A has sample mean of 152.3 and a sample standard deviation of 1.83. Another random sample of 8 observations from population B has a sample standard deviation of 1.94. Assuming equal variances in those two populations, a 99% confidence interval for μA − μB is (-0.19, 4.99), where μA is the mean in population A and μB is the mean in population B. (a) What is the sample mean of the observations from population B? (b) If we test H0 : μA ≤ μB against Ha : μA > μB, using α = 0.02, what is your conclusion?
If continuous random variable normally distributed with mu = 256.43 and J = 27.11 , what is P(225.75 <= x <= 300.35) ?
Suppose that X₁,..., Xn is a random sample from a distribution with probability den- sity function 2 ) = { +/- - - fx(x) = √3/₂e-x/0, 0 0. You are provided the information that the maximum likelihood estimator of is Ô i=1 = 2n (You do not need to derive this mle.) (a) Verify that Fisher's information in the random sample is given by 2n In (0) 02
An electrochemical engineer has manufactured a new type of fuel cell (a type of battery)which has to undergo testing to prove its duration: the time it takes to go from fullycharged to completely uncharged, under a fixed nominal load. From the computational simulation models she has, the variance of the duration is σ2 = 4 h2 (hours squared)but she wants to estimate the mean duration time μ. To achieve this she is determinedto do the tests multiple times in independent but identical conditions. Can you findwhat is the smallest number of these tests that she has to do in order for her estimatedmean duration to be within ±0.2 h tolerance of the true mean with 95% certainty
You obtain 336 successes in a sample of size n1=391n1=391 from the first population. You obtain 419 successes in a sample of size n2=472n2=472 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the test statistic for this sample
We have a random variable X1 for population 1 with a mean value of 52 and standard deviation of 3. we have a random variable X2 for population 2 with a mean value of 50 and population standard deviation of 4. we obtain a random sample of 625 elements independently for both populations. what is the probability that the difference in the sample averages X1-X2 is at least 2.3?
Solve with R, please

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