IEE 380 Ch 3 Discrete Uniform Distribution

so this is going to be a pretty short little video about our first um named distribution called the discrete uniform distribution you've actually already seen this the throw the face value for the throw of a fair die actually adheres to something called the discrete uniform distribution my apologies I'm recording this at night

and uh there's some Shadows coming in here so I hope that's not going to be a problem so if we have a random variable X and it takes on N different possible values here so I just called them little X1 little X2 again these are lowercase uppercase with equal probabilities we say that it has the discrete uniform

distribution and notice that if the range is the range is commas here then we know that it's a discrete random variable we also know it's discrete because it says it's discrete and it's also chapter three now if these are consecutive integers then this is how we can actually um we can express the probability Mass

function of X this is how you usually see it as consecutive integers sometimes you see it um by the way as follows you might see it as 1 over B minus a plus one and that's for X going from a A plus one and again if these are consecutive integers this is what it would be

if they're consecutive integers so this is no different than this here it's just a different way to express it if I want to get the expected value of a discrete uniform then I just apply the regular formula like I did for any other discrete random variable I have the mean equals the expected value of again you

see uppercase X I take all of my x's I multiply them by their probabilities and if I do that for this particular distribution I end up with as if these are consecutive integers X1 plus x n over two if I do it and I see that my distribution looks like this then I