Types of Probability Distribution [Explained with Examples]
Updated on Mar 01, 2024 | 8 min read | 19.5k views
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Updated on Mar 01, 2024 | 8 min read | 19.5k views
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Anyone interested in data science must know about Probability Distribution. Data Science concepts such as inferential statistics to Bayesian networks are developed on top of the basic concepts of probability. So to enter into the world of statistics, learning probability is a must.
Data Science is currently one of the most in-demand interdisciplinary fields to watch out for. Of late, there has been a lot of buzz around the same, thanks to its immense application depth and broad coverage for a number of domains.
Data science, simply put, extracts insights as well as facts from semi-structured and structured datasets with the use of methods, scientific approach, algorithm as well as related tools. These data-based results and insights can be used as means to improve production, and business expansion, while also helping in anticipating the user’s needs. Such probability distribution or probability distribution types are vital as you perform data analysis while preparing datasets for model-based training. In the article, you will get to understand finer details about probability distribution types plus other types.
Statistics is analysing mathematical figures using different methods.
It gives us a more holistic view of different numbers. Statistics for data science is very crucial. Data science is all about figures, and statistics make it simpler and comprehensive.
Probability is an intuitive concept. We use it unknowingly in our daily life. Probability is the measure of how likely an event occurs. For example, if there is a 60% chance of rain tomorrow, then the probability is 60%.
The concept of probability distribution types is very significant in terms of statistics and how it works. It comes with immense uses across applications for engineering, medicine, and business, among many other domains.
Most uses for types of probability are related to making future predictions as per samples for any random experiments. For instance, in the case of business, the types of probability could be used to predict profits and losses to a company as per the latest strategy. It can also be used to prove hypotheses in medical fields based on the varying types of probability.
A probability distribution is represented in the form of a table or an equation. The table or the equation corresponds to every outcome of a statistical experiment with its probability of occurrence.
Probability distributions can be calculated even for simple events, such as tossing a coin.
The following table shows the probability distribution of each outcome of tossing a coin each outcome with its probability.
Number of heads | Probability |
0 | 0.25 |
1 | 0.50 |
2 | 0.25 |
They can also be for complex events, such as the probability of a certain vaccine successfully treating COVID-19.
To know about probability distributions, you must know about variables and random variables.
Usually, a capital letter denotes a random variable, and a lower-case letter denotes one of its values.
For example,
For example, P(X = 1) is the probability that the random variable X is equal to 1.
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Statisticians divide probability distributions into the following types:
Discrete probability functions are the probability of mass functions. It assumes a discrete number of values.
For example, when you toss a coin, then counts of events are discrete functions because there are no in-between values. You have only heads or tails in a coin toss. Similarly, when counting the number of books borrowed per hour at a library, you can count 31 or 32 books and nothing in between.
Thus, if you toss a coin, the occurrence of head denotes success, and a tail denotes failure.
The probability function is px(1-p)1-x where x € (0, 1)
Poisson distributions have the following assumptions:
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It is also known as probability density functions. There is a continuous distribution if the variable assumes to have an infinite number of values between any two values. Continuous variables are measured on scales, like height, weight and temperature.
When compared to discrete probability distributions where every value is a non-zero outcome, continuous distributions have a zero probability for specific functions. For example, the probability is zero when measuring a temperature that is exactly 40 degrees.
Suppose the random variable X assumes k different values. Also, P(X=xk) is constant.
The P(X=xk) = 1/k
Suppose you toss a coin, then what is the probability of the outcome to be one or fewer heads. This is a cumulative probability.
How Do You Find Expected Value Plus Standard Deviation For Types Of Probability Distribution?
You will be able to find the expected value as well as the standard deviation for any probability distribution type once you have the formula, the probability for the distribution or a sample.
Do keep in mind that nominal variables will not have expected values or standard deviations.
This expected value is just a name for the mean of the distribution. It’s mostly written like E(x) or µ. When you take up any random sample of distribution, you must expect the sample mean to be roughly equal to the expected value.
When you have a formula describing this distribution, like a probability density function, then the expected value is given by the µ parameter. When there’s no µ parameter for the types of probability distribution, the expected value will be calculated from other parameters using equations specific to every distribution.
When there is a sample, the mean of that sample is the estimated expected value of the population’s probability distribution. The larger the sample is in terms of size, the better the estimate.
Number of heads: x | Probability P(X=x) | Cumulative Probability: P(X ≤ x) |
0 | 0.25 | 0.25 |
1 | 0.50 | 0.75 |
2 | 0.25 | 1.00 |
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