IEE 380 Ch 3 Bernoulli Binomial Distributions

this video is going to talk about two distributions the first one is necessary for the second one to exist and the first distribution is called the Bernoulli distribution we often refer to it as a Bernoulli trial and it's when we are doing some we call it an experiment or some situation that results in only

one of two possible outcomes we usually say that their pass or fail or success or fail and we usually um assign a probability of P here to a success which we typically say our random variable X is equal to one for a success and one minus P we associate with X is equal to zero as a failure it

doesn't have to be success or failure it can be you know Dead or Alive it can be passes or doesn't pass it can be anything it just has to have two outcomes and this is what our probability Mass function of X looks like right here so X can only be two different values again this is a

lowercase x the expected value of a Bernoulli trial if you go through it and you go you say oh okay this will be zero times one minus P plus one times P you see that the expected value is just the success probability I'm going to let U you do that one and then I will tell you

that the variance works out to be if you do it all right it works out to be P times 1 minus P so the variance is the success probability times the failure probability and there's a couple different ways if we have I just wanted to graph it a little bit so if this is

zero and this is one and this is X and this is my probability Mass function if we had a situation where the success probability was less than the failure probability then it would look something like this again Blades of grass here and this would be at a height of p and this would be at a height of 1 minus P