Discrete Probability

When we study probability we play with words like chance, class, and objects. We assume that the events might have an unlimited number of outcomes. But then came the process of discrete probability that can easily count the number of occurrences whose outcomes or chances can be limited. 

Some examples of discrete probability are like the playing cards or the snooker balls because all the different types of experiments that we do with the playing cards or the balls have a definite number and that number can easily be taken into account by using the concept of discrete probability. 

Mathematics of Discrete Probability 

Apart from the examples that are given in the above paragraphs, there are some other examples of discrete probability also that are specifically related to maths like the Poisson distribution. If we want to go into more depth then the processes of the binomial distribution and Bernoulli distribution can also be categorized under the process of discrete probability but we will learn about all these processes later.  

With the simple example of a coin toss, we can explain that when we toss a single coin, the probability of heads coming and the probability of tails coming are the same and that probability is a number whether you take it as fifty percent or half each infraction. Hence, it is the easiest example of discrete probability. 

Terms regarding the discrete probability

If we are to learn this concept in full depth we will have to learn about different types of terms that are associated with discrete probability. The first term is the probability mass function and it is stated that all the random variables when involved in the process of discrete probability have a finite value. 

The second term is called the categorical distribution and it states that all the random variables associated with the process of discrete probability may or may not have a finite value but each one of them has a finite set of values. The last term is the relative frequency distribution, which states that all the values in the set will have to be divided by the number of outcomes possible for that particular set. 

The last term is called frequency distribution and it is one of the most common terms used across the concept of probability. The term frequency distribution stands for the number of times a particular outcome comes in a sample. 

Important probability distributions

This topic is one of the most important topics when we study the concept of discrete probability. There are a lot of probability distributions generally but we will not study all of them. This process involves subjects like the birth rate, literacy rate, and the population of any particular country, city, and state. These topics are the only ones included as these things go through a lot of changes in a very short period. 

This is because there is not much time in the interval between a child being born or a student being declared to be literate and all these other processes. Now we learn about other types of probability distributions like linear growth and exponential growth.  

Linear Growth and Exponential Growth 

It is also the most important and the most frequently used method in the concept of probability distributions. It is the process that is used when we take into account only a single quantity. The moment we have to start taking multiple quantities into the picture, the process of linear growth does not work. For that process to work, we will go through another process. 

For multiple quantities, we study the process known as exponential growth. This process is also in turn divided into two sub-processes namely Pareto distribution and long normal distribution. The process of Pareto distribution is used when we have to go through multiple quantities but the catch here is that the quantities have to be distributed exponentially whereas we use the process of the long normal distribution when we have to distribute the multiple quantities normally and we do not have to involve the concept of exponents and powers in it. 

Concept of Poisson Distribution

The concept of Poisson distribution involves three different processes in it, namely, gamma distribution, exponential distribution, and the process of categorical distribution. The process of Poisson distribution states that it counts the occurrences of the type of Poisson type events in a particular sample space. 

The process of exponential distribution includes the time or frequency by which the Poisson events occur and finally, the gamma distribution includes the number of times the Poisson events occur but the fact that makes it different from the process of the exponential distribution is that every categorical distribution is that the frequency of that event has to be multiplied by a constant, k, which is usually dependent upon the frequency of the event that has occurred. 

The Poisson Events 

The probability of a mass function is called a Poisson event. This allows the researcher to observe any number of events at a particular period. This process is independent of the type of event that is being experimented upon. 

Conclusion 

The process of discrete probability is one of those concepts that involve basic terms like that of class, objects, and many more. This is one of those concepts that involves many things like exponential distribution and Poisson distribution.