In general, in studying n-trials associate with a two event happening, one would
examine the binomial expansion
(p+q)n=
∑n
j=0
(n
j
)
pn−jqj
and the term within this expansion having the form
(
n
m
)
pmqn−m=nCmpmqn−m=
n!
m! (n−m)!p
mqn−m (11 .38)
represents the probability that the event will happen mtimes in ntrials.
Discrete and Continuous Probability Distributions
The estimated probability of an event is taken as the relative frequency of occur-
rence of the event. As the number of observations upon which the relative frequency
is based increases, then the discrete probability is replace by a continuous function
f(x)called the probability function or probability density function of the distribution
with the condition that the total area under the probability density function must
equal unity. The figure 11-5 is a graphical representation illustrating this conversion.
Figure 11-5.
Discrete frequency function replaced by continuous probability distribution.
