IEE 380 Ch 4 Std Normal and Normal Distributions

- [Instructor] So, for the next few minutes, we're gonna be talking about the normal distribution, which is another continuous probability distribution, and also a special form of it, which is called the standard normal distribution. The normal pdf has a mean that we're gonna call mu, just like we always do in a variance

that we'll call sigma square, just like we always do in a standard deviation that we call sigma, just like we always do. The probability density function, it is symmetric. It goes from negative infinity to positive infinity, and I can use any combination of these inequalities and it all means exactly the same thing.

There are two calculator functions that you're gonna wanna familiarize yourself with if you have the TI series, that's what I have here, but most other calculators have them. If I am interested in computing the probability or the cdf of the... If I wanna compute the cdf, I'm gonna use something called the normalcdf,

and I'm gonna integrate from negative infinity, 'cause that's the lowest value that x can be up to the value that I'm interested in under the mean and the standard deviation. So, when I'm computing the pdf of a normal distribution, so this is infinity, this is the mean, this is minus infinity, capital F of x is gonna be,

just pick any x here, lemme use even a different color. So, if I pick an x here, then this area here, that is what we call capital F of x. It's the probability X is less or equal to this value or less than that value. So, kinda gotta know what this thing means, right?

Now, so, this function, this normalcdf, this is gonna compute right here. This computes a probability. That means it's gonna return a value somewhere between 0 and 1. Now, suppose I wanted to get the value of x for a given area. So, right here. Then I'm going to use this function called the inverse norm.