We have the following information about the random variables X and Y:0.25, oμχ=1, με=-1.5, oX==Calculate the variance of Z = 3X + 5Y,=a) when the coefficient of correlation is p(X, Y) = 0.46:0²2 27.71X: 1.b) when X and Y are independent random variables:0²/2 27.75

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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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Two computer companies are offering new software to universities. Let X and Y denote the number of software installed in three major universities by these two companies. Suppose that the variance of X is 539, the variance of Yis 754, and the covariance of X and Yis 183.50. a) Calculate the correlation coefficient (p) Select one: a. 0.287 b. 0.857 c. None of the answers d. 0.928
18. Two random variables have the regression equations : 3 X+2Y - 26 = 0 6X+ Y- 31 = 0 Find the mean value and the coefficient of correlation between X and Y. If the variable of X 25, find the standard deviation of Y from the data given above. tem (be scue)
Two random variables X = (1,2) and Y= (-2,-1] are equiprobable and independent. Determine the correlation factor r(X,Y),
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There are two random variables X and Y, and their correlation coefficient pX,Y = 0.7. Now, we have two new random variables A = 2.5X+1 and B = 4Y+2. Please compute the correlation coefficient of A and B, PA,B Please round your answer to one decimal place.
A computer while calculating the correlation co-efficient between the variables X and Y obtained the following values. N = 25 )X= 125 SX2 = 650 2y= 100 EY2 = 460 EXY = 508 It was, however, later on discovered at the time of checking that it had copied down two pairs of observations as : X Y 14 8 While actual values were Y 12 8 Obtained the correct value of correlation coefficient between X and Y.
A set of n = 5 pairs of X and Y scores has SSX = 18, SSY = 8, ∑X=5, ∑Y=15, SSCP = 3. What is the Pearson Product Moment correlation for these scores? answers: a) 18/12 = 1.50 b) 18/144 = .125 c) 3/12 = .25 d) 3/144 = .21
Calculate estimates of the standard deviations sz, Sy of the samples r = (5,9, 7) and y = (-1,2,5) as well as the Pearson coefficient of correlation rry of r and y. Which of the following answers are correct? a) sz = 4, sy = 9 b) rzy = 0 c) sz = 2, sy = 3 d) Tzy = } e) rzy =
n,T 3. Suppose {uit}i=1,t=1 be i.i.d. variables with mean zero and variance o?. Show that for each i, Auit is autocorrelated. That is, Auit is correlated to some of its past values. E.g., it is enough to calculate Cov (Auit, Auit-1) and Cov (Auit, Auit-2) to see if any of these are non-zero.
We are researching the charity donation behaviour of Australians. We have the following model: (E1) Donate = β0 + β1Income +β2Avg_Gift + β3Edu + u Where: Donate is a dummy variable equal to 1 if the individual makes a donation in response to a social media campaign by our charity organisation, and 0 otherwise Income is the annual household income Avg_Gift is the average value of past donations made by the individual to our charity Educ is the individual's level of education (in years) Our data is a random sample of the population and we have 1,614 observations. You should assume E [u | Income, Avg_Gift, Educ] = 0. Using the information above, please answer the following 3 questions. [i] Referring to Model (E1) above, interpret the coefficient β1. [ii] You know that this model will suffer from heteroskedasticity. Why is this the case? Explain your reasoning. [iii] In your own words, what is heteroskedasticity?

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We have the following information about the random variables X and Y: 2 1, μY = -1.5, o = 0.25, o} = 1. Calculate the variance of Z = 3X + 5Y, a) when the coefficient of correlation is p(X, Y) = 0.46: μχ = 02²/2 = 27.71 X b) when X and Y are independent random variables: 0²/ = 27.75 X