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Applications of Mathematical Distributions in Daily Life


In Mathematics, a mathematical function called the distribution function which gives the probability of occurrence of the various experimental outcomes. There are different types of distributions. Some of them are:

Binomial Distribution
Normal Distribution
Poisson Distribution
Chi-Square Distribution

The above-mentioned distributions are called probability distributions. These are the important distributions in Maths, which are used for finding the probability of the experiment. Apart from these distributions, some other distributions are gamma distribution, beta distribution, uniform distribution, lognormal distributions, exponential distribution, geometric distributions and so on. Here, let’s discuss the real-time applications of the several probability distributions.

Probability Distributions with its Applications

Binomial Distribution:

Medical and Military Operations
Quality Control
Scientific works

Poisson Distribution:

Used in call centres to maintain the number of phone calls/minute
Finding the number of spelling mistakes while typing in a single page

Normal Distribution:

Error Corrections
Social science
Physical science
Guiding instrument in the research process
Interpretation and analysis of data obtained from the experiment

Chi-Square Distribution:

Testing for homogeneity
Goodness of fit
Testing for attributes independence.

Exponential Distribution:

Queuing theory
Reliability theory
Examining the decay of radioactive particles

Gamma Distribution:

Used as a modelling tool in the counting process
Queuing Models
Financial Services

Lognormal Distribution:

Distribution of the dust concentration in the atmosphere
Rainfall analysis

Each distribution is characterised by its properties. We know that the different types of numbers in Maths is characterised by its properties such as associative property, commutative property, distributive property and commutative property. Likewise, the probability distribution also follows certain properties such as:

The sum of probabilities of all the possible outcomes should be equal to 1
The probability value ranges between 0 and 1
The distributions should describe the dispersion of the random variable value.
A random variable is of two types, such as a discrete variable or the continuous variable
Probability Mass Function (PMF) defines the distribution of a discrete random variable
Probability Density Function (PDF) explains the distribution of the continuous random variable.

All the probabilities mentioned above should fall under either discrete distribution or continuous distribution.

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