Fill out the table giving the joint and marginal PMFs for X and Y.Find E[X] and E[Y].Find the covariance of X and Y.Are X and Y independent? 3. Let X be a uniform random variable that takes values -2, -1, 0, 1, 2. Let Y = X².Y\X-2-112PY14Px(a) Fill out the table giving the joint and marginal PMFs for X and Y.(b) Find E[X] and E[Y].(c) Find the covariance of X and Y.(d) Are X and Y independent? Explain.

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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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Fill out the table giving the joint and marginal PMFs for X and Y.

Find E[X] and E[Y].

Find the covariance of X and Y.

Are X and Y independent?

3. Let X be a uniform random variable that takes values -2, -1, 0, 1, 2. Let Y = X².
Y\X
-2
-1
1
2
PY
1
4
Px
(a) Fill out the table giving the joint and marginal PMFs for X and Y.
(b) Find E[X] and E[Y].
(c) Find the covariance of X and Y.
(d) Are X and Y independent? Explain.

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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