L08.9 Calculation of Normal Probabilities
We have claimed that normal random variables are very important, and therefore we would like to be able to calculate probabilities associated with them. For example, given a normal random variable, what is the probability that it takes a value less than 5? Unfortunately, there are no closed form expressions that can help us with this. In particular, the CDF, the Cumulative Distribution Function of normal random variables, is not given in closed form. But fortunately, we do have tables for the standard normal random variable. These tables, which take the form shown here, give us the following information. If we have a normal random variable, which is a standard normal, they tell us the values of the cumulative distribution function for different values of little y. In terms of a picture, if this is the PDF of a standard normal and I give you a value little y, I'm interested in the corresponding value of the CDF, which is the area under the curve. Well, that value, the ...