If the time of capture [tau](x) is a continuous random variable
with density, [p.
For a continuous random variable
f(x) interpreted as dF(x)/dx is the probability density function (pdf).
Let X be a continuous random variable
with probability density function f (x), the basic measure of uncertainty is given by Shannon  and is defined as
We say that X is continuous random variable
if its place of results is some interval and if its distribution function F(x) in this interval can continuously be derived.
Rounding of continuous random variables
and oscillatory asymptotics.
Distributions of discrete and continuous random variables
frequently used in applications
Subsequent chapters cover countable and uncountable sample spaces, continuous random variables
, functions of one and two random variables, conditional probabilities for countable sample spaces and continuous random variables
, Bernoulli, geometric and Poisson processes, Brownian motion and white noise, and convergence of random variables.
With examples, illustrations and accessible text Stapleton describes discrete probability models, special discrete distributions, continuous random variables
, special continuous and conditional distributions, moment generating functions and limit theory, estimation, testing of hypotheses, the multivariate normal (as well as chi-square, t and F distributions) nonparametric statistics, linear statistical models, and frequency data.
The topics are basics of probability, discrete and continuous random variables
, statistics, hypothesis testing, simple regression, and nonparametric statistics.