6-ConceptsProbability Page 200 Wednesday, February 4, 2004 3:00 PM
200 The Mathematics of Financial Modeling and Investment Management■ The variance of a random variable measures the average size of its fluc-
tuations around the mean.
■ The correlation coefficient between two variables is a number that
measures how the two variables move together. It is zero for inde-
pendent variables, plus/minus one for linearly dependent determin-
istic variables.
■ An infinite sequence of random variables might converge to a limit ran-
dom variable. Different types of convergence can be defined: pointwise
convergence, convergence in probability, or convergence in distribu-
tion.
■ Random variables can be added to produce another random variable.
■ The characteristic function of the sum of two random variables is the
product of the characteristic functions of each random variable.
■ Given a multivariate distribution, the regression function of one ran-
dom variable with respect to the others is the conditional expectation
of that random variable given the values of the others.
■ Joint normal distributions admits a linear regression function.