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Consider the following joint probabilities table for X and Y , where x = 1, 2, 3 and y = 1, 2, 3, 4. X\Y 1 2 3 1 2 3 4 0.05 0.1 0.05 0.01 0.2 0.02 0.25 0.07 0.15 0.01 0.03 0.06 Calculate the covariance of X and Y. Cov(X,Y)= 0.4584 X Calculate the standard deviations of X and Y. σχ 0.6771 = σy = 1.2459 X Calculate the coefficient of correlation of X and Y.

Consider the following joint probabilities table for X and Y , where x = 1, 2, 3 and y = 1, 2, 3, 4. X\Y 1 2 3 1 2 3 4 0.05 0.1 0.05 0.01 0.2 0.02 0.25 0.07 0.15 0.01 0.03 0.06 Calculate the covariance of X and Y. Cov(X,Y)= 0.4584 X Calculate the standard deviations of X and Y. σχ 0.6771 = σy = 1.2459 X Calculate the coefficient of correlation of X and Y.

A First Course in Probability (10th Edition)
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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Consider the following joint probabilities table for X and Y , where x 1, 2, 3 and y = 1, 2, 3, 4. X\Y 1 2 3 = Calculate the covariance of X and Y. ox: 1 2 3 4 0.05 0.1 0.05 0.01 0.2 0.02 0.25 0.07 0.15 0.01 0.03 0.06 Cov(X,Y)= 0.4584 X Calculate the standard deviations of X and Y. - 0.6771 oy 1.2459 = X Calculate the coefficient of correlation of X and Y. p(X,Y)= -0.0204 X
Transcribed Image Text:Consider the following joint probabilities table for X and Y , where x 1, 2, 3 and y = 1, 2, 3, 4. X\Y 1 2 3 = Calculate the covariance of X and Y. ox: 1 2 3 4 0.05 0.1 0.05 0.01 0.2 0.02 0.25 0.07 0.15 0.01 0.03 0.06 Cov(X,Y)= 0.4584 X Calculate the standard deviations of X and Y. - 0.6771 oy 1.2459 = X Calculate the coefficient of correlation of X and Y. p(X,Y)= -0.0204 X
Expert Solution
Step 1: calculating covariance
X\Y1234Marginal Total
10.050.10.050.010.21
20.20.020.250.070.54
30.150.010.030.060.25
Marginal Total0.40.130.330.141

Formula for covariance is given by:

C O V left parenthesis X comma Y right parenthesis equals E left parenthesis X Y right parenthesis minus E left parenthesis X right parenthesis asterisk times E left parenthesis Y right parenthesis

E left parenthesis X right parenthesis equals sum from blank to blank of X P left parenthesis X right parenthesis equals 1 asterisk times 0.21 plus 2 asterisk times 0.54 plus 3 asterisk times 0.25 equals 2.04 space space space space left parenthesis space a s space w e space n e e d space t o space c a l c u l a t e space f o r space e v e r y space x space s o space w e space h a v e space u s e space m a r g i n a l space t o t a l space o f space x right parenthesis E left parenthesis Y right parenthesis equals sum from blank to blank of Y P left parenthesis Y right parenthesis equals 1 asterisk times 0.4 plus 2 asterisk times 0.13 plus 3 asterisk times 0.33 plus 4 asterisk times 0.14 equals 2.21 N o w comma E left parenthesis X Y right parenthesis equals 1 asterisk times 1 asterisk times left parenthesis 0.05 right parenthesis plus 1 asterisk times 2 asterisk times left parenthesis 0.1 right parenthesis plus 1 asterisk times 3 asterisk times left parenthesis 0.05 right parenthesis plus 1 asterisk times 4 asterisk times left parenthesis 0.01 right parenthesis plus space space space space space space space space space space space space space space space 2 asterisk times 1 asterisk times 0.2 plus 2 asterisk times 2 asterisk times left parenthesis 0.02 right parenthesis plus..... plus 3 asterisk times 3 asterisk times 0.03 plus 3 asterisk times 4 asterisk times left parenthesis 0.06 right parenthesis space space space space space space space space space space space equals 4.48 C O V left parenthesis X comma Y right parenthesis equals E left parenthesis X Y right parenthesis minus E left parenthesis X right parenthesis asterisk times E left parenthesis Y right parenthesis equals 4.48 minus 2.04 asterisk times 2.21 space space space space space space space space space space space space space space space space space space space equals negative 0.0284



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