(13) Let a, b, c, d be constants. If all of the following covariances are well defined then show that Cov(aX + bY, cZ + dW) = ac Cov(X,Z) + ad Cov(X, W) + bc Cov(Y,Z) + bd Cov(Y, W). The following outlines of the proofs are proposed, where U = aX + bY and V = cZ + dW. ca) Cov(U + V) = Cov(U) + Cov(V), which gives the result. (b) Since Cov(UV) = Cov(U)Cov(V), the result follows by substituting U = aX + bY and V = cZ + dW. %3D (c) All we need to do is use the definition of covariance, then multiply out the expressions inside the expectation operation, E(UV), and then use the linearity of expectations to get this result. d) The result, as stated, is false. (et None of the above

(13) Let a, b, c, d be constants. If all of the following covariances are well defined then show that Cov(aX + bY, cZ + dW) = ac Cov(X,Z) + ad Cov(X, W) + bc Cov(Y,Z) + bd Cov(Y, W). The following outlines of the proofs are proposed, where U = aX + bY and V = cZ + dW. ca) Cov(U + V) = Cov(U) + Cov(V), which gives the result. (b) Since Cov(UV) = Cov(U)Cov(V), the result follows by substituting U = aX + bY and V = cZ + dW. %3D (c) All we need to do is use the definition of covariance, then multiply out the expressions inside the expectation operation, E(UV), and then use the linearity of expectations to get this result. d) The result, as stated, is false. (et None of the above

Name: Problem 13 (13) Let a, b, C,d be constants. If all of the following co
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Description: Problem 13 (13) Let a, b, C,d be constants. If all of the following covariances are well defined then show thatCov(aX + bY, cZ + dW) = ac Cov(X, Z) + ad Cov(X, W) + bc Cov(Y,Z) + bd Cov(Y, W).The following outlines of the proofs are proposed, where U

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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Problem 13

(13) Let a, b, C,d be constants. If all of the following covariances are well defined then show that
Cov(aX + bY, cZ + dW) = ac Cov(X, Z) + ad Cov(X, W) + bc Cov(Y,Z) + bd Cov(Y, W).
The following outlines of the proofs are proposed, where U = aX + bY and V = cZ+dW.
(a) Cov(U + V) = Cov(U) + Cov(V), which gives the result.
(b) Since Cov(UV) = Cov(U)Cov(V), the result follows by substituting U = aX +bY and V = cZ + dW.
(c) All we need to do is use the definition of covariance, then multiply out the expressions inside the expectation operation, E(UV), and then use the linearity of expectations to get this result.
(d) The result, as stated, is false.
(e) None of the above
(a)
(b)
(c)
(d)
(e)
N/A
(Select One)

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