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With the rule above we can compute the expectation of a random variable X with a Bin(n,p)

which can be viewed as sum of Ber(p) distributions:

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Var(X + Y) is generally not equal to Var(X) + Var(Y)

If Cov(X,Y) > 0 , then X and Y are positively correlated. If Cov(X,Y) < 0, then X and Y are negatively correlated.

If Cov(X,Y) =0, then X and Y are uncorrelated.

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In general, E[XY] is NOT equal to E[X]E[Y].INDEPENDENT VERSUS UNCORRELATED.

If two random variables X and Y are independent, then X and Y are

uncorrelated.

The variance of a random variable with a Bin(n,p) distribution:

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The covariance changes under a change of units

The covariance Cov(X,Y) may not always be suitable to express the dependence between X and Y. For this reason, there is a standardized version of the covariance called the correlation

coefficient of X and Y, which remains unaffected by a change of units and, therefore, is dimensionless.

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