A Breakdown of Binomial Distribution
In probability there are several ways to analyze data in order to make inferences and draw conclusions. Generally, every instance in probability falls under a type of distribution. Once you identify the distribution type, you can easily follow the steps prescribed for it and start your analyses.
What is a distribution? A good definition for it is — a function in statistics that shows the possible values for a variable, and how often it may occur. Distributions are portrayed graphically with histograms, which make them fairly easy to understand. A common type of distributions is the binomial distribution. Below is a visual of what it looks like.
The binomial distribution is used when there are exactly two mutually exclusive outcomes of a trial. For example, a coin toss has only two possible outcomes: heads or tails, as well as taking a test which you can either pass or fail.
For a distribution to be binomial, there are a few conditions it must meet.
1. There are “n”, a specific number of trials.
2. The probability is equal in each trial.
3. Each trial is independent, and do not have an effect on each other.
4. There are only two possible outcomes: success or failure.
Once the binomial conditions are met, the probability, or “p” of “x” successes in “n” independent trials is given by the formula included above. A term that is important to binomial distributions is the probability mass function. It pretty much consists of a discrete number of values, and it can only sum up to 1.
Some of the mathematical properties for this distribution such as the mean, is equal to n * P. In addition, the standard deviation for the binomial distribution is the square root of n*p*q.
A real world application of binomial distribution, for example, would be with pharmaceuticals. Researchers usually come up with new medicines to test and the probability of the specific medicine to work on a patient has discrete outcomes: it either works on them, or doesn’t work at all. A binomial distribution can also be used in the case of whether a Republican or Democrat will win the race for presidency. In the business world, banks and other financial institutions use binomial distribution to determine the likelihood of borrowers defaulting, how much money to keep in the reserve, or even how much to loan. It is a very important type of probability distribution.
Many random instances that are worth examining have two outcomes. In data science, it is a concept that must be fully understood especially when dealing with probability and statistical analysis of data.
