Need help pls Consider the following joint probabilities table for $ X $ and $ Y $, where $ x = 0, 10 $ and $ y = 90, 100, 110 $.\[\begin{array}{c|ccc}X\backslash Y & 90 & 100 & 110 \\\hline0 & 0.05 & 0.27 & 0.18 \\10 & 0.15 & 0.33 & 0.02 \\\end{array}\]Calculate the coefficient of correlation of $ X $ and $ Y $.\[\rho(X, Y) = \boxed{}\] **Explanation of Table:**- The table shows joint probabilities for combinations of values of $ X $ and $ Y $.- For $ X = 0 $ and $ Y = 90, 100, 110 $, the probabilities are 0.05, 0.27, and 0.18 respectively.- For $ X = 10 $ and $ Y = 90, 100, 110 $, the probabilities are 0.15, 0.33, and 0.02 respectively.**Task:** - Use the provided joint probabilities to calculate the correlation coefficient between $ X $ and $ Y $.

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

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Need help pls

Consider the following joint probabilities table for $ X $ and $ Y $, where $ x = 0, 10 $ and $ y = 90, 100, 110 $.

\[
\begin{array}{c|ccc}
X\backslash Y & 90 & 100 & 110 \\
\hline
0 & 0.05 & 0.27 & 0.18 \\
10 & 0.15 & 0.33 & 0.02 \\
\end{array}
\]

Calculate the coefficient of correlation of $ X $ and $ Y $.

\[
\rho(X, Y) = \boxed{}
\]

**Explanation of Table:**
- The table shows joint probabilities for combinations of values of $ X $ and $ Y $.
- For $ X = 0 $ and $ Y = 90, 100, 110 $, the probabilities are 0.05, 0.27, and 0.18 respectively.
- For $ X = 10 $ and $ Y = 90, 100, 110 $, the probabilities are 0.15, 0.33, and 0.02 respectively.

**Task:**
- Use the provided joint probabilities to calculate the correlation coefficient between $ X $ and $ Y $.

Expert Solution

Step 1: Introduce the given information

Here the given joint probabilities table for X and Y is :-

$X vertical line Y$	90	100	110	Total
0	0.05	0.27	0.18	0.50
10	0.15	0.33	0.02	0.50
Total	0.20	0.60	0.20	1

We have to calculate the coefficient of correlation of X and Y.

Using formula,

$rho open parentheses X comma Y close parentheses equals fraction numerator C o v open parentheses X comma Y close parentheses over denominator square root of V a r left parenthesis X right parenthesis times V a r left parenthesis Y right parenthesis end root end fraction$