s_dist1 http://www.openmath.org/cd/s_dist1.ocd 2003-04-01 2001-03-12 2 0 official relation1 calculus1 interval1 arith1 nums1 fns1 arith1 fns1 This CD holds the definitions of the basic statistical functions used on random variables. It is intended to be `compatible' with the MathML elements representing statistical functions. mean This symbol represents a unary function denoting the mean of a distribution. The argument is a univariate function to describe the distribution. That is, if f is the function describing the distribution. The mean is the expression integrate(x*f(x)) w.r.t. x over the range (-infinity,infinity). mean(f(X)) = int(x*f(x)) w.r.t. x over the range [-infinity,infinity] sdev This symbol represents a unary function denoting the standard deviation of a distribution. The argument is a univariate function to describe the distribution. The standard deviation of a distribution is the arithmetical mean of the squares of the deviation of the distribution from the mean. The standard deviation of a distribution is the arithmetical mean of the squares of the deviation of the distribution from the mean. 2 variance This symbol represents a unary function denoting the variance of a distribution. The argument is a function to describe the distribution. That is if f is the function which describes the distribution. The variance of a distribution is the square of the standard deviation of the distribution. The variance of a distribution is the square of the standard deviation of the distribution. 2 moment This symbol represents a ternary function to denote the i'th moment of a distribution. The first argument should be the degree of the moment (that is, for the i'th moment the first argument should be i), the second argument is the value about which the moment is to be taken and the third argument is a univariate function to describe the distribution. That is, if f is the function which describe the distribution. The i'th moment of f about a is the integral of (x-a)^i*f(x) with respect to x, over the interval (-infinity,infinity). the i'th moment of f(X) about c = integral of (x-c)^i*f(x) with respect to x, over the interval (-infinity,infinity)