![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
expand_more
expand_more
format_list_bulleted
Question
thumb_up100%
Please see attached statistical mathematics question. How to find the constant c so that the signicance level is alpha = 0.05.
and determine the power
![Let \( Y_1 < Y_2 < Y_3 < Y_4 \) be the order statistics of a random sample of size \( n = 4 \) from a distribution with probability density function (pdf) \( f(x; \theta) = \frac{1}{\theta}, \) for \( 0 < x < \theta, \) and zero elsewhere, where \( \theta > 0 \). The hypothesis \( H_0: \theta = 1 \) is rejected and \( H_1: \theta > 1 \) is accepted if the observed \( Y_4 \geq c \).
- **Objective**: Find the constant \( c \) such that the significance level is \( \alpha = 0.05 \).
- **Additionally**: Determine the power function of the test.](https://content.bartleby.com/qna-images/question/5aa4cb66-a2f7-4199-af14-322b31fac275/ec2c391b-7b3f-4418-88f8-7555892b3989/x17xy8b_thumbnail.jpeg)
Transcribed Image Text:Let \( Y_1 < Y_2 < Y_3 < Y_4 \) be the order statistics of a random sample of size \( n = 4 \) from a distribution with probability density function (pdf) \( f(x; \theta) = \frac{1}{\theta}, \) for \( 0 < x < \theta, \) and zero elsewhere, where \( \theta > 0 \). The hypothesis \( H_0: \theta = 1 \) is rejected and \( H_1: \theta > 1 \) is accepted if the observed \( Y_4 \geq c \).
- **Objective**: Find the constant \( c \) such that the significance level is \( \alpha = 0.05 \).
- **Additionally**: Determine the power function of the test.
Expert Solution
![Check Mark](/static/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 2 steps
![Blurred answer](/static/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- let X and Y be independent standard normal random variables. Determine the pdf of W = X^2 + Y^2. Find the mean and the variance of U= (1/2)Warrow_forwardLet X and Y be independent Exp(2) random variables. Define W = X + Y. a) Determine the correlation between X and W. The joint pdf of X and W is: fx,w(x, w) = 1^(2) e^(-1w) I{Oarrow_forwardLet Z be a standard normal random variable. Find formulae for thedensities of |Z|, Z^2, 1/Z, and 1/Z^2arrow_forwardLet X1, X2, ..., X„ be a random sample from a Uniform(0,0 +1) population with 0 > 0, *(4)"^( +1) be the median of the random sample. X where n is an even integer. Let M Find the probability density function of the median M. Find the expected value and variance of M.arrow_forwardSuppose that a positive continuous random variable X has probability density function given by f(x)=c(14-5x^2), where c is a constant. What is the variance of this random variable? TYPE YOUR ANSWER AS THE NEAREST NUMBER WITH TWO DECIMAL DIGITS.arrow_forwardLet X be a random variable with pdff(x) = 4x^3 if 0 < x < 1 and zero otherwise. Use thecumulative (CDF) technique to determine the pdf of each of the following random variables: 1) Y=X^4, 2) W=e^(-x) 3) Z=1-e^(-x) 4) U=X(1-X)arrow_forwardFind the mean of the random variable X with PDF S 3x² _if 0arrow_forwardA continuous variable Y has a probability density function for which the moment generating function is given by M(t)=e^(2*t+72*t^2). What is the variance of the variable, Var[Y]?arrow_forwardThe useful life of a concrete built on the seashore has a Weibull distribution of parameter scale δ> 0 year and power β = 2. (δ=21). Determine a) The average life of concrete EXb) The variance VXc) The probability that the concrete lasts more than 10 years; P (X> 10)arrow_forwardLet X be a random variable with p.d.f., fx) = {2e2d-»),x > 1 0 ,x < 1. (1) Find the moment generating function of X (2) Find the mean and variance of X using the mgf from (1).arrow_forwardLet X ~ Uniform(a, b). Find Expected value EX.arrow_forwardThe density of a random variable X is f(x) = C/x^2 when x ≥ 10 and 0 otherwise. Find P(X > 20).arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman