Probability Distributions Explained

In probability theory, a probability density function or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.

For Example:

While tossing a fair (unbiased) coin, there could be a chance of the possibility of two outcomes (“heads” and “tails”), which are equally probable.

Types of Probability Distributions:

There are many different types of probability distribution. Some of them which we will be covering in this blog are listed below:

1) Normal Distribution or Gaussian Distribution

2) Binomial Distribution

3) Poisson Distribution

Normal distribution

Also known as the Gaussian distribution, is a probability distribution that is symmetric around the mean, showing that data near the mean are more frequent in occurrence than data further from the mean. In graph form, normal distribution will appear as a bell curve.

Binomial Distribution:

Binomial is a type of distribution that has two possible outcomes (the prefix “bi” means two, or twice).For example, a coin toss has only two possible outcomes: heads or tails and taking a test could have two possible outcomes: pass or fail. A Binomial Distribution shows either (S)uccess or (F)ailure.

Binomial Distribution is a Discrete Distribution. It describes the outcome of binary scenarios, e.g. toss of a coin, it will either be head or tails.

It has three parameters:

n — number of trials.

p — probability of occurrences of each trial (e.g. for toss of a coin 0.5 each).

size — The shape of the returned array.

The main difference between binomial and normal is that normal distribution is continuous whereas binomial is discrete, but if there are enough data points it will be quite similar to normal distribution with certain loc and scale.

Poisson Distribution

is a Discrete Distribution. It estimates how many times an event can happen in a specified time. e.g. If someone eats twice a day what is probability he will eat thrice? It has two parameters:

rate — known number of occurrences e.g. 2 for above problem.

size — The shape of the returned array.

But we can see that similar to binomial for a large enough poisson distribution it will become similar to normal distribution with certain std dev and mean.

Thanks for reading!

Resources: Statistics with Python Specialization Coursera