Probability: Types of Distributions

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In this lecture we are going to talk about various types of probability distributions and what kind of events they can be used to describe. Certain distributions share features, so we group them into types. Some, like rolling a die or picking a card, have a finite number of outcomes. They follow discrete distributions. Others, like recording time and distance in track & field, have infinitely many outcomes. They follow continuous distributions.

Video Timestamps:

1:29 Discrete Distributions
3:42 Continuous Distributions

We are going to examine the characteristics of some of the most common distributions. For each one we will focus on an important aspect of it or when it is used. Before we get into the specifics, you need to know the proper notation we implement when defining distributions. We start off by writing down the variable name for our set of values, followed by the “tilde” sign. This is superseded by a capital letter depicting the type of the distribution and some characteristics of the dataset in parenthesis. The characteristics are usually, mean and variance but they may vary depending on the type of the distribution. Alright! Let us start by talking about the discrete
ones. We will get an overview of them and then we will devote a separate lecture to each one. So, we looked at problems relating to drawing cards from a deck or flipping a coin. Both examples show events where all outcomes are equally likely. Such outcomes are called equiprobable and
these sorts of events follow a discrete Uniform Distribution. Then there are events with only two possible outcomes – true or false. They follow a Bernoulli Distribution, regardless of whether one outcome is more likely to occur. Any event with two outcomes can be transformed into a Bernoulli event. We simply assign one of them to be “true” and the other one to be “false”. Imagine we are required to elect a captain for our college sports team. The team consists of 7 native students and
3 international students. We assign the captain being domestic to be “true” and the captain being an international as “false”. Since the outcome can now only be “true” or “false”, we have a Bernoulli distribution. Now, if we carry out a similar experiment several times in a row we are dealing with
a Binomial Distribution.

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