The calculator handles random variables. We will use the latter to shorten the discussion below. Cumulants are convenient polynomials of expectations. This greatly reduces the space required for output. Only nonzero terms are printed.
Similar identities relate averages and expectations.
These identities are used to compute transformations between types of expressions. These have the form illustrated by EfromK which produces an expression in terms of expectations from an expression in terms of cumulants. Now the order of E and K in EfromK may seem odd. The transformations are listed below. The following example shows input and output from the applet window.