Find mean and variance of X and Y

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To find the mean and variance of random variables X and Y from a marginal distribution table, the mean is calculated using the formula \(\bar{X} = \sum_i x_i P_X(x_i)\), where \(x_i\) represents the values of X and \(P_X(x_i)\) their respective probabilities. The initial calculations presented for the means of X and Y were incorrect, as they did not apply the proper formula. Variance can be computed using the formula \(Var(X) = E[X^2] - (E[X])^2\), where \(E[X^2]\) is the expected value of the square of X. The correlation coefficient can be derived once the means, variances, and covariance of X and Y are established. Proper application of these statistical formulas will yield the correct results.
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Homework Statement



I have found the marginal distribution for X and Y from a table. (No statistical regression, just simple table)
How should I proceed in finding mean, variance an correlation coefficient of X and y? I am computing by hand.
Thank you,



Homework Equations





The Attempt at a Solution

 

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Is mean for X:

(1/8+3/8+3/8+1/8)
-------------------
4

and mean for Y is

(2/8+4/8+2/8)
--------------
3

?
 
No. Remember the mean of a random variable is defined as

\bar{X} = \sum_i x_i P_X(x_i)

It's the sum of the product of the values X can take on multiplied by probability of that value.
 

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