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 tha 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).

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 tha 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).

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A: Solution

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)
4
10
0.05
0.1
20
0.1
0.1
0.05
0.05
30
0.05
0.15
40
0.1
0.15
0.05
0.05
3
2.

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