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Home » Statistics Homework Help » Theoretical Distribution
Theoretical Distribution
The probability distribution of a random variable may be:

1. Theoretical listing of outcomes and probabilities which can be obtained from a mathematical model representing some phenomenon of interest.

2. An empirical listing of outcomes associated, with their observed relative frequencies.

3. A subjective listing of outcomes associated, with their subjective or ‘contrived’ probabilities representing the degree of conviction of the decision maker as to the likelihood of the possible outcomes.

The observed frequency distributions are based on observations and experimentation. For example, we may study the marks of the students of a class and classify the data in the form of a frequency distribution as follows:

Marks No. of students
0-20 10
20-40 12
40-60 25
60-80 15
80-100 8
Total 70

The above example clearly shows that the observed frequency distribution is obtained by grouping data. They help in understanding property the nature of data. For instance, a shoe-maker must know something about distribution of sizes of his potential customers’ feet; otherwise he may be struck with the shoe size that he cannot sell. Similarly, an owner of a restaurant must know about the peoples’ likes and dislikes of various foods, otherwise he might find heaps of lamb-chops and paucity of streaks.

As distinguished from this type of distribution which is based on actual observation, it is possible to deduce mathematically what the frequency distributions of certain populations should be. Such distributions as are expected on the basis of previous experience or theoretical considerations are known as ‘theoretical distributions’ or probability distributions.

Some of its main topics are:

i. Theoretical distributions
ii. Hypergeometric distribution
iii. Normal distribution
iv. Poisson distribution
v. The multinomial distribution
vi. Ordinates-method

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