![]() Let’s say that this function takes in a number as input, adds 2 to the input number, and returns the new number as output. For the vast majority of cases, the function actually has to do something with the input for the output to be useful. On a very abstract level, a function is a box that takes an input and returns an output. So let’s first define what a function is generally and then we’ll move onto functions used for probability distributions. The function allows us to define a probability distribution succinctly. To get around the problem of writing a table for every distribution, we can define a function instead. Worse still, the number of possible outcomes could be infinite, in which case, good luck writing a table for that. In many scenarios, the number of outcomes can be much larger and hence a table would be tedious to write down. In the above example of rolling a six-sided die, there were only six possible outcomes so we could write down the entire probability distribution in a table. ![]() Introduction to functions Why are we talking about functions? And since this is not an infinite number of values, it means that the support is finite. The support is essentially the outcomes for which the probability distribution is defined. In the specific case where we have 2 variables, we often say that it’s a bivariate distribution.įinite support = This means that there is a limited number of outcomes. In contrast, if we have more than one variable then we say that we have a multivariate distribution. In this case, we only have the outcome of the die roll. Univariate = means that we only have one (random) variable. You can probably guess when we get to continuous probability distributions this is no longer the case. In mathematics, we would say that the list of outcomes is countable (but let’s not go down the path of defining and understanding countable and uncountable sets. For example, if we consider 1 and 2 as outcomes of rolling a six-sided die, then I can’t have an outcome in between that (e.g. I can’t get an outcome that’s in between. That’s a bit of a mouthful, so let’s try to break that statement down and understand it.ĭiscrete = This means that if I pick any two consecutive outcomes. To be explicit, this is an example of a discrete univariate probability distribution with finite support. The probability distribution for a fair six-sided die To give a concrete example, here is the probability distribution of a fair 6-sided die. For example, a random variable could be the outcome of the roll of a die or the flip of a coin.Ī probability distribution is a list of all of the possible outcomes of a random variable along with their corresponding probability values. Recall that a random variable is a variable whose value is the outcome of a random event (see the first introductory post for a refresher if this doesn’t make any sense to you). So I’m going to try to explain what they are in this post. Often it is assumed that the reader already knows (I assume this more than I should). Probability distributions are used in many fields but rarely do we explain what they are. However, probability theory is often useful in practice when we use probability distributions. These are the things that get mathematicians excited. In my first and second introductory posts I covered notation, fundamental laws of probability and axioms. Probability concepts explained: probability distributions (introduction part 3)
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |