joint pr muy Tass Tun p(x, y) = Px (x) (a) Draw a 3 x 3 table showing the joint probability mass function for all possible values of X and Y. Use your table to show that X and Y have the following marginal PMFs. = x = 1 and y = {1,3} x = 3 and y = 2 otherwise 4 0 1 4 x = 1 x = 2 x=3 x, y = {1,2,3} py (y) = 3 8 1 y = {1,3} y = 2 (b) Draw a 3 x 3 table showing px (x) py(y) for all possible values of (X, Y). Are X and Y independent or dependent random variables? (c) Use the marginal PMFs to calculate mean, variance, and standard deviation of X and of Y: μx, μy, Var(X), Var(Y), ox, 0y. (d) Calculate the covariance Cov(X, Y) of the jointly-distributed random variables. (e) Calculate their correlation Corr(X, Y). Are X and Y correlated or uncorrelated?
joint pr muy Tass Tun p(x, y) = Px (x) (a) Draw a 3 x 3 table showing the joint probability mass function for all possible values of X and Y. Use your table to show that X and Y have the following marginal PMFs. = x = 1 and y = {1,3} x = 3 and y = 2 otherwise 4 0 1 4 x = 1 x = 2 x=3 x, y = {1,2,3} py (y) = 3 8 1 y = {1,3} y = 2 (b) Draw a 3 x 3 table showing px (x) py(y) for all possible values of (X, Y). Are X and Y independent or dependent random variables? (c) Use the marginal PMFs to calculate mean, variance, and standard deviation of X and of Y: μx, μy, Var(X), Var(Y), ox, 0y. (d) Calculate the covariance Cov(X, Y) of the jointly-distributed random variables. (e) Calculate their correlation Corr(X, Y). Are X and Y correlated or uncorrelated?
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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Transcribed Image Text:Two discrete random variables X and Y each take integer values from 1 to 3 with the following
joint probability mass function.
p(x, y)
=
px (x)
4
=
3
4
0
X =
4
X =
1 and y = {1,3}
3 and y
otherwise
(a) Draw a 3 × 3 table showing the joint probability mass function for all possible values of X
and Y. Use your table to show that X and Y have the following marginal PMFs.
=
x = 1
x = 2
x = 3
2
x, y = {1,2,3}
py (y)
8
=
تان پر
ye {1,3}
E
y = 2
(b) Draw a 3 × 3 table showing px(x) · py(y) for all possible values of (X, Y). Are X and Y
independent or dependent random variables?
(c) Use the marginal PMFs to calculate mean, variance, and standard deviation of X and
of Y: Mx, My, Var(X), Var(Y), ox, 0y.
(d) Calculate the covariance Cov(X, Y) of the jointly-distributed random variables.
(e) Calculate their correlation Corr(X, Y). Are X and Y correlated or uncorrelated?
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