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Statistical distributions can be either discrete or continuous. The theoretical discrete distribution is defined as the probability distribution that depicts the occurrence of discrete (individually countable) outcomes. The continuous distribution is defined from those outcomes that come on a continuum. The probability distribution of random variable X will be writing the all possible values of x taken by X. It’s probability will be represented by P(x). Here, x takes the value in one trial of the experiment.
Key Notes on Theoretical Discrete Distribution-
Important points to remember are-
The discrete probability distribution counts occurrences that have finite outcomes.
This is in contrast to a continuous distribution, where outcomes can fall apart anywhere on a continuum.
The most common examples of discrete distribution include the binomial, Poisson, and Bernoulli distributions.
These distributions often involve statistical analyses of “counts” of an event.
Understanding Discrete Distribution
Discrete distribution is a concept which is used in research work. It helps in identification of the outcomes of the events from the data points of the data set which will lead to probability distribution diagrams. The normal distribution is one of the example of the probability distribution diagram.
The nature of outcome can be identified by the development of the type of distribution like if it is a discrete distribution or the continuous distribution. The normal distribution is continuous and possible outcomes can be identified along the number line. On the other hand, a discrete distribution is calculated from the data that can have finite number of outcomes.
Hence, The Discrete distribution describes the data having countable number of outcomes which even includes the potential outcomes. The list can be finite or infinite. For example, the probability distribution of the die having six sides numbered as 1,2,3,4,5 and 6, then the list can be written in form of (1,2,3,4,5,6). The binomial distribution have finite set of only two possible outcomes. Those outcomes can be 0 or 1. For example- when a coin is flipped then the probability of two possibilities are Heads or tail. The distribution can be either discrete or continuous.
Examples of Discrete Distribution:
The discrete probability distributions consists of binomial, Poisson, and Bernoulli. The Poisson distribution is used to count data where the tally is small. In other words, it is 0.
The Discrete distributions can also be seen in the Monte Carlo simulation. Monte Carlo simulation is a modelling technique that identifies the probabilities of different outcomes through a high-level programmed technology. It is primarily used to help forecast scenarios and identify risks. In Monte Carlo simulation the outcomes with discrete values will produce discrete distributions only for analysis. These distributions are used in determining risk and trade-offs among different items.
Conclusion-
In this article on theoretical discrete distribution, we have discussed the discrete distribution in detail. We have seen the examples of discrete distribution in detail to understand the concept in a better way. We have also understood the term Monte Carlo simulation and how it is used in finding discrete distribution. We have also gone through the different types of discrete distribution. There are a few requirements of discrete distribution which are the probabilities of random variables must have discrete values as outcomes, for a cumulative distribution, the probability of each discrete observation must be between 0 and 1; and the sum of all the probabilities must equal one.
