IEE 380 Ch 4 Continuous pmf CDF

well now we will start chapter four chapter three was all about discrete random variables and chapter four is about continuous random variables so a reminder about what a continuous random variable is that is a random variable or um it takes on uh it's a it's a uncountable set that means that it is a it has a

range of possible values and it actually has an infinite number of values so I want to write that down infinite foreign number of possible values now we know that the poisson distribution which is discrete has an infinite number of possible values but they're all integer and we call that one countably infinite a continuous random

variable as it says here is not countable you can't um you can't differentiate from one point to the other so common ones would be say the height of a person the volume of Deuce in a can time is almost always considered a continuous random variable the thing is though and I would like to

point this out in the red pen we round values of continuous random variables although they um that that doesn't make it an integer so just a little word of warning here so rounding let's say we rounded a rounding a I'm going to get better red pen here continuous value b-a-l-u-e 2 and integer

and this is the point does not make the value discrete in other words just because we round a continuous random variable doesn't mean that we've made it a discrete random variable so do be careful with that so just like in um with the probability Mass function for a discrete random variable a probability

density function is what we call the probability function for a continuous random variable so we call it the density function so recall like for if if x is discrete so let me write this down just to show you the comparison so I'll write the recall button here or recall word here for discrete we have a probability Mass