Probability:
Probability distribution refers to estimating how likely it is that an event will occur or not and so the probabilities of the event occurring would be between 0 and 1 where there is a 0% chance and then event will not happen and a 1% chance that the event will take place. Now, in order to calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes. There are certain properties of probability that one should be aware of. The first being that the probability of any event is always between 0 and 1. The second property states that the probability of an event that cannot occur is 0. And lastly, the probability of an event which should occur is 1. The terms used for the same are impossible event and certain event respectively.
Types of Probability Distribution:
There are two types of probability distribution: the discrete probability distribution and the continuous probability distribution. A discrete probability distribution refers to the probability of the occurrence of each value of a discrete random variable which means that it is a random variable where it can have countable values, or we can say finite number of values. On the other hand, a continuous probability distribution would refer to the probabilities of the possible values of a continuous random variable and which means that it is a random variable that has a set of infinite number of values.
Types of Discrete Probability Distribution:
o Binomial Probability Distribution
o Poisson Probability Distribution
o Bernoulli Probability Distribution
o Hypergeometric Probability Distribution
Types of Continuous Probability Distribution:
o Normal Probability Distribution
o Student’s t-distribution
o Uniform Probability Distribution
o Exponential Probability Distribution
o Chi-square Probability Distribution
1. Discrete Probability Distribution Example
Binomial Distribution:
It is a type of the discrete probability distribution which represents the probabilities of different values of the random variable in repeated independent n trials in any event taking place. The probability of the binomial distribution is given by the following formula:
Example:
Let’s consider an example for the binomial probability distribution for the IT industry where 80% of all business startups in this industry report that they are generating a profit in the first year so if a sample of 10 new businesses is selected what could be the probability that exactly seven will generate a profit in the first year. In this example, the conditions of the binomial distribution are checked to see if they satisfy with the example mentioned. The conditions are such that there are only two possible outcomes which would generate a profit in the first year or not and there are a fixed number of trails. Thus, the example matches the conditions of the binomial distribution and by computing the value we get a 20.13% probability that exactly 7 out of the 10 IT startups would generate a profit in their first year.
2. Continuous Probability Distribution Example
Normal Distribution:
It is the most commonly used probability distribution in all of the statistics and a type of the continuous probability distribution where it has properties like bell shaped, symmetrical, has one peak, the mean and median are equal i.e., both are located at the center of the distribution and so on. The normal distribution formula is as follows:
where x is the variable, u is the mean and sigma is the standard deviation.
Example:
Let us consider an example related to the technical stock market to understand and apply the conditions of the normal probability distribution. We are aware about the rise and fall in the prices of the shares in the stock market. The falling and hiking in the price of the shares lead to changes in the log values and the stock prices return often form a bell-shaped curve. Now, if the returns are normally distributed then more than 99% of the returns would fall within the deviations of the mean value. Thus, the normal probability distribution and the characteristics of the curve help the analysts and the investors to gain insights about the return and the risk of the shares in the stock market.
References:
Understanding Discrete Probability Distribution. (n.d.). Master of Project Academy, from https://blog.masterofproject.com/discrete-probability-distribution/
Kumar, A. (2021, October 4). Binomial Distribution Explained with Examples. Vital Flux, from https://vitalflux.com/binomial-distribution-defined-with-10-examples/#What_is_Binomial_Distribution
Examples of Binomial Distribution Problems and Solutions. (n.d.). Intellspot, from https://www.intellspot.com/binomial-distribution-examples/
Normal Distribution. (n.d.). BYJU’S, from https://byjus.com/maths/normal-distribution/
Zach, S. (2021d, February 9). 6 Real-Life Examples of the Normal Distribution. Statology.Org, from https://www.statology.org/example-of-normal-distribution/
9 Real Life Examples Of Normal Distribution. (n.d.). Studious Guy, from https://studiousguy.com/real-life-examples-normal-distribution/#:~:text=9%20Real%20Life%20Examples%20Of%20Normal%20Distribution%201,Birth%20Weight.%20.%20.%20.%209%20Student%E2%80%99s%20Average%20Report.%20
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