Suppose that X and Y are two random variables whose moment generating functions can beox(s) = e2s+8s²+. øy(s) = e*+2s² +.written on the formulaThus the exponents states Taylor expansion log, x(s) respectively log, Y(s) around s-0a. Determine the variance of the variable Z=2X-Y+8 if you know that the covariancebetween X and Y if given by Cov(X,Y)=0b. Between which values can the variance Var(Z) vary if there is no condition onCov(X,Y)?

Suppose that X and Y are two random variables having MGF φx(s)=e2s+8s2+... φY(s)=es+2s2+... taking…

Answered: ates Taylor expansion log : variance of…

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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Y has a distribution function (0, ys0, 24 F(y) = 0
Question 2. Show that, for a simple linear regression, R² = ry, where R² is the coefficient of determination and rxy is the sample correlation between Y and X. Hint: Σ" (Υ - Y)2 Σ1(Y₁-Y)²¹ SxY √SXXSYY' where Sxy = 1 (X; — X)(Y; — Y), Sxx = ₁1(X; - X)², Syy = ₁₁(Y₁ - Y)². R² = "XY =
After studying the milk yields of a randomly selected sample of 900 cows, researchers felt that the presence of white spots (WS;) on a cow's body led to a different level of milk production (MP;). The researchers estimate the OLS regression: where WS, is a binary variable of the form: WS₁ = MP = 5.36 +0.26 x WS₁, (2.23) (0.06) 1, if the th cow has white spots 0, if the th cow doesn't have white spots The 95% confidence interval for the coefficient ₁ is (₁). (Round your answers to four decimal places.) Based on this interval, we will the hypothesis P₁ = 0 at the 5% significance level. Which of the following statements describes the way in which the coefficient of the indicator variable could be interpreted in this case? O A. The coefficient is the sum of the conditional expectation of the presence of white spots on a cow with respect to the average milk production. OB. The coefficient is the rate of change in the milk production due to a unit change in the number of cows with white…
Suppose you are to estimate a simple regression for the following population model: Y=B₁ + B₁X + µl From a population of over thousands of observations, a small number of samples were randomly selected. The following is some of the information from the randomly selected sample.
The variance of Y is σ2y = 4.6875 and the variance of the sum is σ2x + y = 9.1875. You knowthe variance of X=1. Find the covariance, xy. Show work
If our data were a perfect fit to our regression model, such that y; = ŷ;, we would expect | to be in the CI on p.
x > 1 A RV X has the PDF fx(x) = otherwise (a) Find the MGF Mx(t) of X and clearly define the values of t for which it exists. (b) Find the mean (µ) and variance (o?) of the RV X using the MGF from (a).
"given a simple regression with slope b=3, s (sub y)=8, and s (sub x)= 2, and n=30. Find the standard error of the estimate."
Suppose you obtain the following regression model, E[y]=91+79*x1 +20*x1*x2. What is the impact of a 39 unit change of x1 on the expected value of y when x2 is at its mean of 40?
3. 1 + x Check whether the following function is a valid pdf? If it is valid, obtain its CDF. If not valid, would scaling by a constant make it valid? If so, make it valid. Obtain its CDF? What is its mean? Variance? ƒ = —exp(-√x)U(x)

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ates Taylor expansion log : variance of the variable Z= HY if given by Cov(Y Y-0