An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table.p(x, y)051000.010.040.0150.060.130.15y100.020.200.17150.100.100.01(a) Compute the covariance for X and Y. (Round your answer to two decimal places.)Cov(x, y) =(b) Compute p for X and Y. (Round your answer to two decimal places.)P =

yRow totals051015P(x)00.010.060.020.100.19x50.040.130.200.100.47100.010.150.170.010.34Column…

Answered: An instructor has given a short quiz…

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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Let X1, X2, and X3 be uncorrelated RVs each with the same mean, µ, and variance, o?. Find expressions for the following in terms of the mean and variance: 1. Cov(X1 + X2, X, + X3). 2. Cov(X1 + X2, X – X2).
1 Find the cross correlation function for the psd Sy (@) XY 25+ w³ *
(b) For each pair of variables, generate the correlation coefficient r. For all pairs involving x1, compute the corresponding coefficient of determination r2. (Use 3 decimal places.) r r2 x1, x2 x1, x3 x1, x4 x1, x5 x1, x6 x2, x3 x2, x4 x2, x5 x2, x6 x3, x4 x3, x5 x3, x6 x4, x5 x4, x6 x5, x6
Consider the following function to determine an indirectly measured quantity T: Z= 10x, + Ibg The variance-covariance matrix of correlated quantities x and x is given as a table below: X2 X 0.885 0.293 Xa 0.293 0.384 Applying the "General Law of Propagation af Variances', what is the standard error of 2?
Let Rand S denote the sample correlation matrix and the sample covariance matrix, respectively. Let D= diag(s.22. Ann). Show that S-DRD/2 Under what conditions can we conclude from the equation above that R D-1/2SD-1/2? Justify your answer.
For a wide sense stationary process: Select one: O a. the covariance is constant O b. all of these O c. the expected value is constant
Define β1 stands for?
Consider data Y1, Y2, . . . , Yn iid∼ Ber(p). Answer parts a and b of the following question. a.) Suppose you observe data y10 = (1, 0, 0, 0, 1, 0, 1, 0, 1, 1). Find the MLE of the fisher information, I(p). Hint: use invariance principle for MLE. b.) Suppose now you run a larger experiment and you observe fifteen 1s in a sample n = 30. Find the MLE of the fisher information, I(p)
prove
For random variables X and Y such that E(X) = 2, E(Y) = 1, E(X²) = 10, E(Y²) = 3, and E (XY) = c, Find: а. Var(3X — 5Y). b. The correlation coefficient between X and Y, p. The range of values of c for which the assumptions of the problem are consistent. С.
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 583, the variance of Y is 752, and the covariance of X and Y is 179. a) Calculate the correlation coefficient (p) Select one: a. o.825 b. 0.270 c. 0.532 d. None of the answers
9. The joint distribution of Y₁ and Y₂ is given below in the table. Y₁ Y₂ 0 1 2 a. Find E(Y1-Y₂) b. Find Covariance (Y₁,Y2) 0 1/9 2/9 1/9 1 2/9 2/9 0 2 1/9 0 0

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