Answered: The data for the joint probability mass…

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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Question

The data for the joint probability mass function of X and Y (two different measurement systems) are
given in the table below.
a) Calculate the marginal distributions of X and Y and plot them.
b) Select one of the Y values from the table and find the conditional probability mass function of X for that
Y value you have selected and plot it.
c) Show whether X and Y are independent or not.
d) Calculate the covariance of (X,Y) i.e. Cov(X,Y)

Y
f(x,y)
10
20
30
40
5
0.05
0.05
0.10
10
0.10
0.05
X
15
0.10
0.15
0.15
0.05
20
0.05
0.10
0.05

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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