Exercise 13. Let X₁,..., Xn~ N(2,02) i.i.d. and Y₁,..., Yn~ N(Hy, 02) i.i.d. with known o².We assume that for each i the random variables X; and Y, are correlated, with Corr(X₁, Yi) = 1/2.Define D₁ = X₁ - Y, for all i E {1,...,n}. Finally, let X, Y and D be the averages of the X₁, Yiand D₁, respectively.a) Show that Cov(X₁,Y)= 02/2.b) Determine E(D₁) and Var(D;).c) Consider the test for Ho: ₂ = Hy which uses the test statisticZ = √n-and which rejects Ho, if and only if |Z| > 1.96. Show that P(type I error) = 5%.

Answered: random variables X, and Y, are…

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 machine Packages shirt in the bags with a mean weight of 3 kg. A random sample for f 20 bags has a mean weight of 3.05 kg with a standard deviation of 0.05kg. From the data given, state the value of a, (I) parameter ii) statistics
How is a t-test related to the t-statistic of a parameter?
An experiment is conducted to compare the maximum load capacity in tons (the maximum weight that can be tolerated without breaking) for two alloys A and B It is Kknown that the two standard deviations in load capacity are equal at 7 tons each. The experiment is conducted on 50 specimens of each alloy (A and B) and the results are X = 75.8. X = 71.8, and X-X=4. The manufacturers of alloy A are convinced that this evidence shows conclusively that Hug and strongly supports the claim that their alloy is superior. Manufacturers of alloy 8 claim that the experiment could easily have given X-X 4 even if the two population means are equal. Complete parts (a) and (b) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Make an argument that manufacturers of alloy B are wrong. Do it by computing P(XA-XB41 PA-HB) P(XA-X > 4) - @
A normal distribution has a mean of u = 50 and 0 = 12 if one score is randomly selected for distribution what is the probability of randomly selectingt a score that is X < 56
llMetro by T-Mobile X Group Work-Worksheet#1 on Ch... 1 of 2 Group Work-Worksheet#1 on Chapter 3 0.14% → 1. The Empirical Rule Based on Data Set 1" Body Data" in appendix B, blood platelet counts of women have a normal/bell-shaped distribution with a mean of 255.1 and a standard deviation of 65.4. (All units are 1000 cells/μL.) Using the empirical rule: -30 2.14% 1:40 PM 13.59% 99.73% 95.44% 68.26% 34.13% 34.13% 13.59% 77% 2.14% -20 -10 Mean lo 20 За a. 68.26% of women with platelet counts are within two standard deviations of the mean? The values are from ( b. 95.44% of women with platelet counts are within two standard deviations of the mean? The values are from ( 000 c. 99.73% of women with platelet counts are within two standard deviations of the mean? The values are from ( 0.14%
A persons blood glucose level and diabetes are closely related XB a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Supposed to after a 12 hour fast the random variable X will have a distribution that is approximately normal with mean of u=87 and a standard deviation of O=25. Note: after 50 years of age both the mean and Standard deviation tends to increase for an adult under 50 after 12 hour fast find the following probabilities A) X is more than 60 B) X is less than 60 C) X is between 60 and 110 D) X is greater than 125 (borderline diabetes starts at 125)
A normal distribution has a mean of μμ= 54 and a standard deviation of σσ=6 What is the probability of randomly selecting a score GREATER than 51? A normal distribution has a mean of μμ= 54 and a standard deviation of σσ=6 What is the probability of selecting a sample of n = 4 scores with a mean more than M = 51? A normal distribution has a mean of μμ= 54 and a standard deviation of σσ=6 What is the probability of selecting a sample of n = 36 scores with a mean more than M = 51?
The Mean of Binomial distribution is 3 and variance is- · Find 4 (i) the value of n (ii) p ( x 21 ) (iii) p (x<7 )
DCX Suppose that an airline quotes a flight time of 2 hours, 10 minutes between two cities. Furthermore, suppose that historical flight records indicate that the actual flight time between the two cities, x, is uniformly distributed between 2 hours and 2 hours, 20 minutes. Letting the time unit be one minute, (a) Calculate the mean flight time (x) and the standard deviation (ax) of the flight time. (Round your answers to 4 decimal places.) ux OX (b) Find the probability that the flight time will be within one standard deviation of the mean. (Round your answer to 5 decimal places.) P = 18 Fo MAR LO 5 li Ⓒ A WD Show
The processing time for the robogate has a normal distribution with mean 23 sec and standard deviation 2sec. Find the probability that the next operation of the robogate will take 27.4 sec or less. The probability is.

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

random variables X, and Y, are correlated, with Corr(X₁, Y₁) € {1,...,n}. Finally, let X, Y and D be the averages of the = 0²/2. Var(D₂). 0 Hz Hy which uses the test statistic 2= √n². f and only if |Z| > 1.96. Show that P(type I error) = 5%.