ADONGO DISTRIBUTION
Consider that the
possible outcomes of a given time period or space n can be divided into two
categories; those that cause a given event to occurs in a particular time or
space and those that do not.
Consider the
probability distribution of a time or a space event that occurs randomly but
has uniform probability of occurrences and if n denote as time or space and xi denote the number of times
the event occurs at a particular time or space. Then, the probability which
follows above characteristics is Adongo probability distribution.
P(x) = [(αx / (x + 1)] [α + (β / x)]x x = 1, 2, 3, ……………….
MEAN
Given Adongo
distribution of successful outcome in time or space n for x times occurrence of
the event. The mean of the distribution is given as;
E(x) = αn
VARIANCE
Given Adongo
distribution of successful outcomes α and failure β in time space n for x times
occurrences of the event. The variance of the distribution is given as;
Var(x) = αβn
CHARACTERISTICS
OF ADONGO DISTRIBUTION
1.
There
are exactly two possible outcomes in a given time or space. We can think of
these two outcome as “success” and “failure”
2.
The
probability of certain number of success during a given interval of times or
space is determine.
3.
The
individual success are independent of one another
4.
The
success will occur uniformly over the entire time or space under consideration.
EXAMPLE
A
firm manufactures long rolls of tape and then cuts the rolls into 12-ft lengths
Extensive
measurement have shown that defects in the roll occurs at random with
probability 0.40
a. What is the probability that a tape has at most 4
defects?
b. What is the probability that a tape has more than 2
defects?
c. If a case contain 3 tapes, what is the probability
that one tape has 4 defects and the two remaining tape have 3 defects each?
SOLUTION
P( x ≤ 4)
= [ (0.4 * 1) / (1 + 1)] [0.4 + (0.6 / 1)]1
+
[(0.4 * 2) / (2 + 1)]
[ 0.4 + (0.6 / 2)]2
+
[(0.4 * 3) / (3 + 1)]
[0.4 + (0.6 / 3)]3
+
[( 0.4 * 3) / (4 + 1)]
[ 0.4 + (0.6 / 4)]4
P(x ≤ 4) = 0.2 * 1 + 0.267 * 0.49 + 0.3 * 0.216
+ 0.32 * 0.09
P(x ≤ 4) = 0.2 + 0.13 + 0.065 + 0.029
P(x ≤ 4) = 0.424
