For decades, statisticians have enjoyed the use of “statistical packages” which
read in a (potentially) large data set, process the observations, and print
out anything from histograms to sample variances, to p-values, to multidimensional
plots. But pity the poor probabilist, who through all those
decades had only paper and pencil for symbolic calculations. The purpose
of this monograph is to address the plight of the probabilist by providing algorithms
to perform calculations associated with univariate random variables.
We refer to a collection of data structures and algorithms that automate probability
calculations as “computational probability.” The data structures and
algorithms introduced here have been implemented in a language known as
APPL (A Probability Programming Language). Several illustrations of problems
from the mathematical sciences that can be solved by implementing these
algorithms in a computer algebra system are presented in the final chapters
of this monograph.