Page 108 - Standard Handbook Of Petroleum & Natural Gas Engineering

Applied Statistics 97

Probability Distributions for Discrete Random Variables
The binomial distribution applies to random variables where there are only two
possible outcomes (A or B) for each trial and where the outcome probability is
constant over all n trials. If the probability of A occurring on any one trial is
denoted as p and the number of occurrences of A is denoted as x, then the
binomial coefficient is given by

and the probability of getting x occurrences of A in n trials is

The cumulative probability of the binomial distribution is given by

For the binomial distribution

P = "P

For np 2 5 and n( 1 - p) 2 5, an approximation of binomial probabilities is given
by the standard normal distribution where z is a standard normal deviate and

The negatiue binomial distribution defines the probability of the k'h occurrence
of an outcome occurring on the xth trial as

and

(text continued on page 102)