Answered: Consider the variables ? and ?. The…

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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Consider the variables ? and ?. The realization of a sample of size 20 is given below (where ? is
the first variable and ? is the second):

(−1.202, 563.024), (2.112, 291.072), (2.827, −893.619), (−0.314, 1321.814),
(−1.477, −91.573), (−6.516, 446.336), (−0.920, −111.487), (3.477, −153.165),
(−7.273, 1076.221), (2.251, 477.931), (−0.713, 909.696), (−0.853, 226.865),
(−3.176, 389.413), (1.913, −47.169), (−1.070, −178.695), (−3.385, 744.486),
(−9.506, 362.670), (−7.004, 364.578), (0.504, 324.975), (2.861, −360.571)

Sketch an appropriate plot that displays the values of these points. Calculate the sample
covariance as well as the sample’s expectations and variances of ? and ?.

Definition Definition Measure of how two random variables change together. Covariance indicates the joint variability or the directional relationship between two variables. When two variables change in the same direction (i.e., if they either increase or decrease together), they have a positive covariance. When the change is in opposite directions (i.e., if one increases and the other decreases), the two variables have a a negative covariance.

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