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DISCRETE DISTRIBUTION
It can be defined as the statistical or probabilistic properties of observable that is either finite or countably infinite pre-defined value. In a continuous distribution, it has an infinite number of outcomes where as in a discrete distribution it is characterized by a limited number of possible observations and so this is frequently used in statistical modeling as well as in computer programming. It is also known as the "discrete probability distribution" and the variables usually take only discrete values.
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A discrete distribution with probability function defined over, 2, ..., has a distribution function is represented as follows
Examples of this kind of probability distributions include a binomial distribution that is a finite set of values. The binomial distribution is used only when both of the following conditions are met such as the test has only two possible outcomes and the sample must be random. Only if both of the conditions are met, one can use this distribution function to predict the probability of the desired result. Another example is the Poisson distribution which is a countably infinite set of values.The concept of probability distributions as well as the random variables is considered as the underpinnings of probability theory as well as statistical analysis.
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It is used mainly in determining the probability of an outcome value without having to perform the actual trials and for example, if we wanted to know the probability of rolling a six 100 times out of 1000 rolls a distribution can be used rather than actually rolling the dice 1000 times.
An association of the outcomes is with corresponding probabilities if the following two conditions are satisfied such as the sum of all the probabilities in the sample space = 1; that is ∑P(X) = 1. The probability of each event must be between 0 and 1 that is 0 ≤ P(X) ≤ 1. The probabilities are found either theoretically or experimentally by observation and the expectation of a discrete distribution E(X) = Mean μ = ∑X.P(X) as well as the variance of the discrete distribution X, σ2= [E(x)]2- μ2.
