What is Probability Distribution: Definition and its Types

Of course, you will be familiar with the term probability distribution in studying statistics. Talking about probability distributions found in statistics, you will know a lot about the sample mean value.

This is because the term is indeed used as a centralization of data.

The probability distribution will describe a variety of different events which are related to the uncertainty of these various phenomena or events.

Thus, this probability distribution can be used by using experiments to determine the sample space and the multiple possibilities in a particular event.

Of course, deep understanding and knowledge are needed to study and understand probability distributions. But what exactly is the probability distribution? How things go about the ins and outs of the probability distribution will be explained in detail below.

Probability Distribution Definition

A probability distribution is a distribution that describes the probability or likelihood of a set of variables instead of their frequency for the application of probability in statistics, namely by estimating the occurrence of opportunities or possibilities associated with the occurrence of an event in several conditions.

On the other hand, if the overall probability of a possible outcome occurs, then all of the possible events will form a distribution.

Probability Distribution Function

The distribution function is a function that gives a probability value to each event that is used for research.

This distribution provides a relationship with the probability for a value taken from a random variable which is then used to determine a discrete random variable. The function is used to represent the probability distribution in the sample space.

This distribution is a fundamental concept in statistics that is used at both a theoretical and practical level. Here are some practical uses of the function;

1. Used to calculate the confidence interval on a parameter and critical area in a hypothesis test.

2. Used for univariate data, i.e., it is often helpful to determine a reasonable distribution model for that data.

3. Used as statistical intervals and hypothesis tests, often based on assumptions about the distribution. Therefore, verifying that the belief is justified for a given data set is necessary before calculating intervals or performing tests based on an assumed distribution.

This is because the distribution can be a more suitable data distribution. However, it can be an adequate model for statistical techniques to produce valid conclusions or results.

Used as a simulation study with random numbers generated from the use of certain distributions that are often needed.

Probability Distribution Characterictics

After explaining the characteristics, what makes this distribution more unique and different from others is the characteristics. The followings are the characteristics and their explanations.

1. Bell or Bell-Shaped Curve

The first characteristic is that it has a bell-shaped curve or bell, which means it has one peak in the middle. Therefore, the calculated mean is the same as the median and mode.

2. Curve Shaped Symmetrical Curve

The second characteristic is the probability distribution and the standard curve in the form of a symmetrical curve with the calculated average.

3. The Curve Decreases in Both Directions

The third characteristic is that the probability distribution has a downward curve in both directions, to the right for positive values to infinity and to the left for negative values to infinity.

4. Horizontal

The fourth characteristic is that if the area is under the standard curve but above the horizontal axis, then it is equal to having a value of 1.

How to Determine Probability Distributions

The following are the steps in determining this distribution;

1. Random Variables

Random variable research describes how the probability or likelihood is distributed over the values of the random variable.

The probability mass function determines the random variable (which is usually denoted by an ‘x’) probability distribution with the symbol f (x), where the process gives the probability or probability for each value of the random variable.

The development of a probability function for a discrete random variable must meet two conditions, namely:

f(x) must be non-negative for any random variable

The sum of the probabilities for each value of the random variable must equal one.

2. Continuous Variables

This variable can assume the value of anything within an interval on the actual number line or in a set of intervals. The random variable will not take on a specific value because there can be an infinite number of them in any break.

However, it is necessary to consider the probability that the continuous random variable will lie within a particular data interval.

Types of Probability Distribution

After understanding various things about the probability distribution, starting from the understanding of the probability distribution, the knowledge of the probability distribution according to experts, what are the functions of the probability distribution, what are the characteristics and characteristics of the probability distribution, you should also know that this probability distribution has various kinds or type.

Two types of probability distributions are used for different purposes by different data generation processes. The first two types of data distribution are the standard or cumulative probability distribution and the binomial or discrete probability distribution.

The following is an explanation.

1. Normal Probability Distribution or Cumulative Probability Distribution

A standard or cumulative probability distribution is also known as a continuous distribution. Within this probability distribution, there is a set of possible outcomes that can take values over a constant range.

For example, if a set of real numbers is a continuous or normal distribution. This is because a distribution of this type will give all possible outcomes of real numbers.

This includes the set of complex numbers, the group of prime numbers, the collection of integers, and so on, which are examples of normal probability distribution.

In real-life scenarios, this normal or cumulative probability distribution also exists. For example, the temperature on a given day is an example of continuous probability.

2. Discrete Probability Distribution or Binomial Probability Distribution

The second type of distribution is the discrete probability distribution or the binomial probability distribution. This discrete or binomial probability distribution occurs when there are discrete results.

It can be exemplified. For example, if a dice is thrown, then all the possible results will be different, and the results will give many results.

The event can also be known as a function of the probability mass. So, the development of this discrete or binomial probability distribution consists of n repeated trials, and the results may or may not occur.


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