IEE 380 Ch 3 Discrete Poisson Distribution

well the last [Music] um discrete random variable that we're going to be talking about is something called the poisson distribution and it has to do with something called a poisson process uh I don't like these Shadows hang on one second here okay let's see if I can keep some of the Shadow off of here so a porcelain

process is what we call a counting process and we use it often when we're counting things and so we have we have a rate though that happens uh it's a constant and we call it Lambda in our poisson process so you'll see that in just a second but the arrivals are the things that we're

counting are purely random so here's examples of um variables that could be part of a poisson process and notice everything starts with the word number number of people who enter a bank each hour so see that Lambda is a rate so we'll have an average rate of people who answer who enter a bank per hour will have a rate

of number of cars that pass through an intersection per minute or a rate of earthquakes and so on and so obviously this last blank is number so we'll have a rate of defects per square meter um and and so on okay so that's called the poisson process and resulting from the poisson process we have something

called the poisson distribution or the poisson it's actually a probability uh Mass function and it looks like this so we've got Lambda which is my rate then we've got this letter T now T is not a random variable I kind of want to make a big deal about that let me get a red pen

here t is not just because of the capital normally um normally I would say that capital letters are random variables but in this case T is not a random variable it's actually going to be a constant it's X that is my random variable here and so we have x to the number of events