Problem 3:If Y has a binomial distribution with parameters n and p, then p₁= is an unbiased estimator of p.Consider another estimator of p given by P2 =a. Show that p2 is biased for p and derive its bias.b. Derive MSE(P₁) and MSE(p₂)

Answered: Image /qna-images/answer/70068233-60ce-4b62-8a0d-c7d872f5de69.jpg

Answered: Problem 3: If Y has a 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

1. Suppose the random variable X follows a Beta distribution with α = 1 and β = 3. (a) Determine the mean and median of X. (b) Determine the variance of X. (c) Find the probability that X >1/3.
hoosing among several different estimators of 0, select one that is unbiased. Example 9.3: Let X₁, X2, ..., Xn be a random sample from a population mean and variance o². Show that the sample variance, - Σ(x₁ - x)² = n-1 is an unbiased estimator of o². 5²
6. Show that 1 s2 E1(Xi – x)² is unbiased estimator of the population variance o? i=1 п-1
ol 106. Use the two scenarios presented in Figure 7.12 to answer the following question about the two sources of variability in ANOVA. 3.5 3.0 2.5 2.0 1.5 (i) HA: P₁ P2 ‡ P3 (iii) HA not all proportions are equal to this po 1.0 Figure 7.12: Within vs Between Variability in ANOVA onnisth Scenario A L (d) Recall that, O 2 H 3 2.05 2.10 2.15 2.20 2.25 2.30 2.35 (ii) Ho: M₁ M₂ = μ3 sans are (iv) HA: not all means are equal 720 qeaoluet alt sot mol 4 mobor 2924 (6) 2 3 4 gob za aim onbala (1) di batt (9) w-qodt fonqtotal bac o2 (6) (Troy ote12. (0) (a) Which scenario provides stronger evidence that the difference in factor level means represents true differences in the population means? Explain why in your own words. Scenario B 1 = stogol 05 O 1 oftaltete fest out of sulav gris I (b) Which scenario exhibits more variability within each factor level? Is this measured by SSError or SSFactor? Agulow (c) Which scenario exhibits more variability between each factor level? Is this measured by…
3. An integer is randomly chosen from the set 1, 2,..., 100. If this integer is divisible by 2 we let Y = 0, and if it is not divisible by 2 but is divisible by 3 then Y = 1. We let Y = 2 in all other cases. Find mean and variance of Y.
Suppose that x and y are unknowns with ?(?)=E(X)= 11, var(?)=Var(X)=4, ?(?)=E(Y)= 7 and var(?)=Var(Y)= 100. In addition, suppose that the correlation coefficient of ?Xwith ?Yis .6. Then what is the expected value of xy?
1. Which of the following is NOT true when we set α = .05a. Then we accept as significance any outcome that has a 5% chance of making a Type I Error.b. Then we accept as significance any outcome that has a 5% chance of making a Type II Error.c. Has more statistical power than when α = .01.d. All of the above are correct.

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

Problem 3: If Y has a binomial distribution with parameters n and p, then p₁= is an unbiased estimator of p. Consider another estimator of p given by p2=+ a. Show that p2 is biased for p and derive its bias. b. Derive MSE(P₁) and MSE(p₂)