1. Chapter 10: Covariance and Correlation
CIS 2033 based on Dekking et al. A Modern Introduction to Probability and Statistics Slides by Gustavo Orellana Instructor Longin Jan Latecki
Chapter 10: Covariance and Correlation
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2. Gustavo Orellana

3. which can be viewed as sum of Ber(p) distributions:
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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4. 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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5. 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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6. 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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7. 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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