Likelihood Estimation - THE MATH YOU SHOULD KNOW!

hello everyone and welcome to a special episode of code emporium where we're going to talk about likelihood so likelihood is one of those terms where it is proportional to a probability but it is not quite a probability and it's pretty confusing so we're going to walk through some intuition walk through a formal definition and then also we're

gonna work through a lot of math and so i have my trusty pen here so let's get to it all right so let's actually start this discussion by explaining the difference between probability and likelihood so right now i'm going to draw a 2d graph we have the y-axis and the x-axis over here and this x-axis

i'm gonna say is going to represent prices of houses so let's say that this could be two hundred thousand dollars then we have four hundred thousand dollars then we have six hundred thousand dollars and this x-axis just goes on and then the y-axis is going to represent a probability which i'm going to represent

as p of x and let's say that you know for some given population we just know that the distribution of all house prices will look something like this blue curve where you have a lot of examples that probably have middle to to lower prices but then there's like a few examples when you get to the tail end that'll be

like really expensive houses and for all intents and purposes let's say that this is going to be some log normal distribution or something very close to it which means that well we can represent this here with a mean and a standard deviation which we'll call mu and sigma now because this is a probability

distribution we know that it can exhibit certain properties like one such property is that the total area under this blue curve is going to be one so in fancy mathematical notation we could write that as the integration over all x and it's going to be the probability p of x d x now this entire integration for over all