Is there any basis why probability distribution has to be talked about?
What are its uses in understanding data?
Can it show a sense of relevance according to one’s needs?
These are some of the questions that one has to ask in studying probability statistics.
Taking into consideration all of the questions above, it is better to have an overview of the use of histogram as this can directly answer them.
This histogram summarizes certain data. It must be taken note of that the primary function of the histogram is to show a summary of variation in measured data. One might wonder whether a certain curve comes from a distribution or from any other mathematical computation that approximates the histogram. The fundamental idea here is that this histogram fits a probability function. The curve made is an attempt to show probability distribution. Technical know-how of probability is the core concept and even one of the critical building blocks in getting to more advanced analytics and machine learning.
Going deeper, it is better to understand some of the basic concepts:
Its values are subject to changes because it depends on randomness. In other words, a chance process is a determinant factor in the selection of samples. It can take on many possible numbers or items. For example, in choosing five (5) representatives of a group with ten (10) members, random picking of names written on a rolled pieces of papers.
In this, everybody is given an equal chance to represent the group, but not all can be chosen. However, even after the extremities are determined, in this case, the five representatives, there is still no definite description as to who or what the outcome is. This is because there is no exact definition of the outcome as the latter is just a representative of the whole.
In the example given, it is true that five representatives are chosen, but they do not necessarily carry the exact definition of the other five (5) members not chosen. In other words, the description that can be provided is the probability-state base.
By definition, discrete probability describes the probability of occurrence of each value of a discrete random variable. Bear in mind that discrete random variable always has countable values.
This is their reason why the best way to present this is through a table. Colloquially speaking, this is based on chances. For example, in tossing a coin, there is fifty per cent (50%) chance of getting a tail. Understanding the unsaid, there is also 50 per cent (50%) chance of getting a tail. This is called a binary distribution.
If there are 6 six persons who are tasked to roll a dice to get number 6, each one of them has 1/6 chance of getting number 6. What is distinct about this kind is that when you add all the values of all probabilities, you can always arrive at one. Consider the table below:
Actually, there is the same concept as in the discrete distribution. The possible outcomes are in the x-axis and the probabilities are in the y-axis. However, unlike discrete contribution wherein you can find countable values, in a continuous distribution, the description is based on continuous random variables. A continuous random variable is infinite and uncountable. Using the same example as used above, it is not possible to use this kind of distribution in tossing a coin.
The reason is that one cannot arrive at having half tail or half head. There is really no possibility that its continuous random variable can equal any value. In other words, the probability that X is exactly equal to some value is always zero. This is the basic idea behind it.
Let’s take the following example that describes the height of American women (ages 30-39):