U7. Let U › N(0, 1) and V ~ x²(v). If U and V are independent than has a student√V/vT-distribution with degrees of freedom. Using this result prove that the statistic Twe used in the two-sample T test, has T-distribution under the null hypothesis. If thetwo sample sizes are m and n, what is the degrees of freedom of T?

Given that U~N0,1 and V~χ2ν If U and V are independent, then UVν has a student T-distribution with ν…

Answered: 7. Let U~ N(0, 1) and V~ x²(v). If U…

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

Suppose you have a sample of 9 observations Y1,...,Y, from a normal population with mean 2 and variance 4. Let Y and S denote the sample mean and sample variance, respectively. What is the distribution of E ( (a) (b) 653 (c) Suppose X1,X2, X3, X4, X5 are independent random variables from a normal population with mean 0 and variance 4. Define S3 = E(X, - X). What is the distribution of 253 + S3?
Say that we have a null hypothesis that X1,..., X16 that are Normally distributed with mean 0 and variance 1. Call the sample mean X. Consider the test where p-value = 20 (4 X) - 24 (4|X) – 1 We will reject this if p-value < a. a) Show that the type I error rate of this test is a. b) Say that X1,..., X16 that are Normally distributed with mean 1 and variance 1. What is the type II error rate of this test when a = 0.05? •..
Let X1, X2, *. Xn be a random sample of size n from norm population with mean and unknown a. Let X and s be the sample mean and sample standard deviation. Then for any 0
5. When Y,,Y,..,Y, is a random sample from N(u,0). we learned in class that the Y-u statistic T = has t distribution with n-1 degrees of freedom, where Y and S are the sample mean and sample standard deviation, respectively. Write out the form of T² and show algebraically that T can be written as the ratio of two independent z random variables, each divided by their respective degrees of freedom. What is, therefore, the distribution of T? (5 pts.)
Q2: Let x1,X2, . , Xn and y1, y2, ..., Ym represent two independent random samples from the respective normal distributions N(H1,07) and N (H2, 03). It is given that of = 30, but ožis unknown. Then 1. A random variable that can be used to find a 95% confidence interval for - is (x- y) - (H1 - H2) А. ns3 + ms n+m. 3(n+m-2)"tm, nm O A (x – y) – (41 – H2) В. ns? + ms; n + m. (n + m – - 2) пт (x – y) – (41 - H2) С. ns3 + mS;_n+3 3(n+ m-2) ("+3m nm Ос
Let X and Y be independent random variables with μX = 3, σX = 3, μY = 2, and σY = 3. Find the mean and variance of X – Y. The mean of X - Y is . The variance of X - Y is .
Let X and Y be independent random variables such that Var[X] = 4.8 and Var[Y ] = 9.7. How can we prove that 2X and 3Y are independent? What is the standard deviation of 2X + 3Y?
3. If x1, X2, X3, ..., Xn is a random sample from a normal 1 distribution N (µ, 1) show that t= E xí is an unbiased estimator of n i = 1 H² + 1.
The farmers' association of the Amatole region in the Eastern Cape wants to report on the average milk production in this region. It has been shown that the milk production in this region is normally distributed with mean u and variance o?. Suppose a random sample of farms,Y1, Y2, Y3, Y4 is taken from the region. Consider the following estimators of 0: 01 = Ỹ and ô, = 2Y½+2Y3 1. Identify the parameter of interest. 2. You have been presented with two estimators of the parameter of interest. (a) Find the expected value of each of the estimators. (b) Find the variance of each of the estimators.
In a random sample of 320 cars driven at low altitude, 40 of them exceeded the standard 10 grams of particulate pollution per gallon of fuel consumed. In another independent random sample of 80 cars driven at high altitude, 20 of them exceeded the standard. Let P 1be the true proportion of cars that exceed the standard in low altitudes and P 2be the true proportion of cars that exceed the standard in high altitudes. What is the test statistic for testing this hypothesis.
Let X1, X2, X3, be a r. s. from normal distribution with mean 0 and variance 1, let the prior distribution of 0 is normal with mean zeroand variance 1. Let L(6,0) = (ô - 0). Find the Bayes estimator of 0
2. Review on estimators. Let Y = (Y1, 2, 3, 4) be a random sample from the normal distribution N(μ, 2²), where the expected value of the normal distribution μER is unknown, and the variance parameter has four (4) as a value. We examine the following parameter μ estimator 1 ₪ (Y) = ± ± (Y₁ + Y₂ + Y3 + 2Y₁) 4 Calculate the bias of the estimator (Y). Is the estimator unbiased? Calculate the variance and the mean squared error (MSE) of the estimator. The problems deal with the confidence intervals (Chapter 5 topics) and especially testing theory (Chapter 6).

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