IEE 380 Ch 3 Discrete Mean Variance Std Dev

so this lecture is going to show us how to compute the mean and the variance and the standard deviation of a discrete random variable now these all have um deeper meanings than just the mathematical formulas that I'm going to show you but for right now what we need you to do is to be able to understand

that the mean of a discrete random variable on the variance and the standard deviation of a discrete random variable are all handled with certain formulas so here if we fill in the blanks it says that X is a discrete random variable with a probability Mass function P of X remember that the text

uses just a reminder that the text uses scripted f of x but I use Little P of x um the population mean which sometimes we also call average and sometimes I don't use the word population but the mean of X it's also called the expected value of X an expected value has an actual

formula it's given by this equation so the mean is sometimes also referred to as Mu so we have the mean mu is also called the expected value of x and this is uppercase and we're going to get that by summing over all of my values in the range of X that's a lowercase x we take x times the

probability that my lowercase x equals that value it will have the same units as our random variable X so if we're measuring um millimeters then the expected value of will be also in millimeters now if I want to compute the variance so the the mean is actually the long run average if everybody kind of understands

what average is it's variance in standard deviation that are a little bit more difficult to um kind of wrap your head around the variance is as the um you know layman's terms here it is the average squared distance that each value Little X is from the mean so that's what this formula is here now this is called