 two but if you have access to one note we're in the icon left hand side one note presentation 1510 uniform distribution dice tab we've also been uploading transcripts to one note so that you can go into the view tab immersive reader tool change the language if you so choose being able to either read or listen to the transcripts in multiple different languages using the time stamps to tie in to the video presentations one note desktop version here in prior presentations we thought about how we can represent and describe different data sets both mathematically using calculations such as the average the mean the median the quartiles and so on and pictorially using box and whiskers as well as histograms the histograms often being what we visualize when we're thinking about the distribution of the data and then using terms to describe the distribution of the data in the histogram such as skewed to the right skewed to the left and so on what we would like to think about now is the families of curves and formulas that we can put together that can often characterize certain data sets and if we can do that if we can represent a data set with some kind of curve some kind of formula it gives us more predictive power over that data set so that's kind of the goal that we would like to have if we can say hey this data set looks like it can be characterized at least approximately with some kind of line or some kind of curve that we have a formula for that would be a useful tool to have now the first one that we're going to look at the first family of curves will be the uniform distributions it's going to be the easiest one because it's basically a straight line so when we said uniform distributions you might have imagined that we're going to kind of distribute out uniforms for the accounting instruction statistics course and you're going to get a uniform or something no we're talking about uniform distribution as a family of a curve basically representing data all right so we're going to be thinking about dice rules here to get an idea of what this will look like so let's say we have a die and the die has six sides to it and if we were to roll the die a thousand times and what would be the the likelihood that any one number whether that number be a one two three up to six what's the likelihood that we roll how many ones or what's the likelihood to roll a one each time for example well it would be one over six which would be the sixteen point six six on and on so if I rolled it a thousand times what would be basically the expected value that you would have for any one number it would be this times one thousand right times a thousand so you would expect there'd be 166.66 and so on of each individual number of one through six that would be kind of our visualized outcome in our mind now note that this visualized outcome is just a model we're just we're coming up with a model that hopefully provides us some predictive power but of course is not perfect in real life which is clearly described to us by the fact that we have an un whole number here so it would be impossible for our predictive model to actually become true because we can't there's no way that we're going to get a point six seven of a one that or a two that we've rolled right we can't roll it point six seven times but you can see that the model gives us predictive power over what what possible what the chances are in the future so if we take then