Her topics include

discrete random variables and expected values, moments and the moment-generating function, jointly continuously distributed random variables, hypothesis tests for a normal population parameter, quantifying uncertainty: standard error and confidence intervals, and information and maximum likelihood estimation.

Discrete random variables V = {[X.sub.1], [X.sub.2], ..., [X.sub.n]} are assigned to the nodes variables representing a finite set of mutually exclusive states and annotated with a Conditional Probability Table (CPT) that represents the conditional probability of the variable given the values of its parents in the graph.

Roughly speaking, continuous random variables are found in studies with morphometry, whereas

discrete random variables are more common in stereological studies (because they are based on the counts of points and intercepts).

The above definition applies to

discrete random variables; for random variables with continuous probability distributions differential entropy is used, usually along with the limiting density of discrete points.

The inverse transform method can be adjusted for

discrete random variables as well, if we consider the generalized inverse of the cdf i.e.

Toward this goal, we begin by approximating the sequence of single period log normal random variables in (2) by a sequence of

discrete random variables. In particular, assume the information set at date t is ([S.sup.i.sub.t], [h.sup.i.sub.t]), i = 1,2, and let [y.sup.i.sub.t] = ln([S.sup.i.sub.t].), i = 1,2.

general

discrete random variables. A distribution and its PGF are denoted by Pr{[S.sub.n] = k} = [s.sub.k] (k [greater than or equal to] 1) and S(z) = [[summation].sup.[infinity].sub.k=1] [s.sub.k][z.sup.k], respectively.

Among the topics are

discrete random variables and probability distributions, joint probability distributions and random samples, tests of hypotheses based on a single sample, simple linear regression and correlation, and distribution-free procedures.

The text begins with sets and functions, then covers combinatorics, probability, conditional probability,

discrete random variables, and densities.

Theorem 4 (7, Theorem IX.8) Let ([X.sub.n)n [greater than or equal to]1] be a sequence of

discrete random variables supported by N, with associated probability generating functions [p.sub.n](u).

Walker, An efficient method for generating

discrete random variables with general distributions, ACM Trans.

Let in general X and Y be

discrete random variables taking values x = ([x.sub.1],..., [x.sub.n]) and y = ([y.sub.1],..., [y.sub.n]) with a common set of probabilities [Mathematical Expression Omitted], pertaining to a set of relevant states of nature 1,..., n.