Consider the following population model that satisfies the CNLRM assumptions:Y = βX; + uin particular assume that:ui ~ Ν (0,1)What is the mean and variance of B₁?Ε (βι) = 0,6%, = nΣα22 xΣτΟΟΟΣΧΕ (βι) = 0,6% = nΣ #Ε(β) = 1,6 =Ε(βι) = 1,6% = nΣ #(31){"2 ΣβιηΣΧCannot be determined with the information provided.

Answered: Image /qna-images/answer/c99c82f3-abc2-4fce-89dc-14e02d5f17bd.jpg

Answered: Consider the following population model…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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QUESTION 2 i) If U, and U, each have a normal distribution with mean 0 and variance 20². Furthermore, mu, (t) = etio for i = 1,2. Show that U and U2 are independent.
There is a relationship between the following variables as y = 1 / (a * x ^ b) (x ^ b: means x over b). a) Calculate the correlation coefficient and interpret the degree of the relationship? b) Estimate the y value for x = 4.3 and the x value for y = 0.90 by obtaining the regression equation. x 1.2 1.5 2.0 3.0 4.0 5.0 y 0.58 0.50 0.32 0.18 0.15 0.10 x 1.2 1.5 2.0 3.0 4.0 5.0 y 0.58 0.50 0.32 0.18 0.15 0.10
For theoretically modelling the economic development of national economy scenarios the following 2 models for GDP increment are analysed: a. Yt = Yt-1 + at b. Yt = 1.097 Yt-1 - 0,97 Yt-2 + at, where Y - GDP increment a - White noise with zero mean and constant variance o2 =100 t- Time (quarters starting with Q1, 1993) Check by an algebraic criterion which one is stationary.
Two random variables X = (1,2) and Y= (-2,-1] are equiprobable and independent. Determine the correlation factor r(X,Y),
Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.
Explain at least two differences between the following two point estimations of the population variance. 22 = Σ'1(X, – X)2 n-1 62 _ Σ 1 (X - X)2 =1 = n
Let X₁, X2, X3, Xn be a random sample with unknown mean EX; = µ, and unknown variance Var(X₂) = o². Suppose that we would like to estimate 0 = μ². We define the estimator as 2 • - (™)² - [ 2x]* Xk to estimate 0. Is an unbiased estimator of ? Why?
4
The quality characteristic of a product Y consists of three components X1, X2, and X3. The distributions of these components are normal with means 100, 2, 1 and variances 1, 1, 1 respectively. The specifications of the product are 90 ± 8. If Y= X1 + -7X2 + -9X3. Products that are below the lower specification limit are scrapped. Find the proportion of scrapped products = Ф(z).
We calculate the correlation between the percent of adult population fully vaccinated for COVID-19 and the COVID-19 death rate per 100,000 in 2021 for the states and territories of the United States (55 observations). We observe a correlation r=-0.3558 Test the hypothesis H_0: ρ=0 against H_a: ρ≠0 at the 99% level (α=.01)
Let yit denote the outcome of a random variable for the i-th individual at time and let Xit denote a covariate measure on the i-th individual at time t, t, i = 1, ..., n, t = 1,..., T. The data could be modeled using the simple linear regression model: Yit = Bo + B₁xt + Eit, Eit~N(0, t) a) Explain why using this approach may be inappropriate. b) Write a mathematical expression of the random intercept model and the random coefficients models as alternatives to this model. c) Provide an expression for the proportion of variance attributable to each of the variance components in the random coefficients models. d) Write out an expression for the likelihood, priors and posterior for the model in part (c) e) Write out a WinBUGS code for this problem.
Consider a randomized block design involving three treatments and two blocks. Define all variables. X1 X2 Treatment 1 2. 1 3 Let x, = 0 if ---Select-- v is in effect and 1 if --Select--- v is in effect. Write a multiple regression equation that can be used to analyze the data. E(y) =

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