Chapter 10: Covariance and Correlation MATH 3033 based on Dekking et al. A Modern Introduction to Probability and Statistics. 2007 Slides by Gustavo Orellana Instructor Longin Jan Latecki Chapter 10: Covariance and Correlation Gustavo Orellana

Gustavo Orellana

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: Gustavo Orellana

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. Gustavo Orellana

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: Gustavo Orellana

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. Gustavo Orellana