6. Need help Consider the following joint probabilities table for X and Y, where x1, 2, 3 and y = 1, 2, 3, 4.X\Y123=Calculate the covariance of X and Y.ox:12340.05 0.10.050.010.20.020.25 0.070.15 0.01 0.03 0.06Cov(X,Y)= 0.4584 XCalculate the standard deviations of X and Y.-0.6771oy 1.2459=XCalculate the coefficient of correlation of X and Y.p(X,Y)= -0.0204 X

X\Y1234Marginal Total10.050.10.050.010.2120.20.020.250.070.5430.150.010.030.060.25Marginal…

Answered: Consider the following joint…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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6. Need help

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\Y	1	2	3	4	Marginal Total
1	0.05	0.1	0.05	0.01	0.21
2	0.2	0.02	0.25	0.07	0.54
3	0.15	0.01	0.03	0.06	0.25
Marginal Total	0.4	0.13	0.33	0.14	1

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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