Guys I am having trouble with the standard normal distribution.
We know the X values run from approx -inf to +inf but what are the y values?? The normal distrubiton takes two parameters N(mean, variance) but what is the range of y?
y>0 obviously and the "y" will depend on the mean and variance you picked as y=exp(-z^2)/sqrt(2*pi*var). But I have trouble understanding what it means. If I take the S&P500 and I difference the series (SPX-SPX(-1)) the histogram of the returns will have an apporixmate normal distributions and will list out the number of times I have a return of -1%,-.5%,0%,.5%, 1% , etc throughout the history. So is the "y" of the normal distribution the number of times I have had that x as a value? Should I think of the normal distribution in practical terms the number of times that one point event has occurred? I look at some normal distributions and the Y ranges from 0-4, others I see the y ranging from 0 to 1, as a probability should. I know the area underneath the curve should sum to 1 but shouldnt the y values always be less than 1?