Information Technology Reference
In-Depth Information
In the Table, the number of products examined is the total number of
products examined in one sample. The number of qualified products is the total
number of qualified products in the examination. The frequency of qualification
is the proportion of qualified products in all the products examined in one sample.
From the Table, we can easily see that the relation of the number of a mark and
the frequency of a mark. We can also find a statistical regularity. That is, as the
number of products examined increases, the frequency of qualification inclines to
0.9 stably. Or the frequency of qualification wavers around a fixed number
=
0.9. So p is the statistical stable center of this series of trials. It represents the
possibility of qualification of an examined product. The possibility is called
probability.
p
Definition 6.1
Statistical Probability: if in numbers of repeated trials the
frequency of event A inclines to a constant p stably, it represents the possibility of
appearance of event A, and we call this constant p the probability of event A,
shortly by P(A).
p = P(A)
So a probability is the stable center of a frequency. A probability of any event A
is a nonnegative real number that is not bigger than 1.
0
P(A)
1
The statistical definition of probability has close relation with frequency and
is easily understood. But it is a tough problem to find the probability of an
arbitrary event with experiments. Sometimes it is even impossible. So we often
calculate
probability
with
classical
probabilistic
method
or
geometrical
probabilistic method.
Definition 6.2
Classical Probability: Let a trial have and only have finite N
possible results, or N basic events. If event A contains K possible results, we call
K/N the probability of event A, shortly P(A)
P(A) = K/N (6.2)
To calculate a classical probability, we need to know the number of all the
basic events. So classical probability is restricted to the cases of finite population.
In the case of infinite population or the total number of basic events unknown,
geometrical probability model is used to calculate probability. Besides,
geometrical probability also gives a general definition of probability.
Geometrical random trial: Assume
is a bounded domain of M-dimensional
space, and L(
) is the volume of
. We consider the random trial that we throw
a random point into
evenly and assume: (1) Random point may fall in any
domain of
, but cannot fall outside of
. (2) The distribution of random point in
is even, viz. the possibility that random point falls into a domain is
