Probability and Statistics - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 53

1.0

.5

P=.1

.2

P=.05

.1

.05

P=.01

.02

P=.005

P=.001

.01

.005

P=.0005
P=.0001

.002

.001

.0005

.0002

.0001

.00005

.00002

.00001

n = Sample Size

Fig. 2.2 Size of random sample ( n ) needed to detect a species occurring with proportional
abundance ( p ) with probability of failure to detect its presence fixed at P (After Dennison and
Hay 1967 ) (Source: Agterberg 1990 , Fig. 3.1)

2.2.4 Other Discrete Frequency Distributions

Suppose that a succession of Bernoulli trials is started by randomly selecting black
or white cells from a black-and-white mosaic (e.g., an array based on pixels). One
may ask the question of how many times the trial must be repeated before X

¼ Σ m

X i ¼ r where r is a fixed positive integer number and m represents the number of

trials it takes to obtain r . It is convenient to write m k + r where k is another integer

number. The probability of a one (for a black cell) at the m -th trial is p .
This probability must be multiplied by the probability that there were exactly
k zeros (for white cells) during the preceding m -1 (

¼

¼ k+ r 1) experiments.