update readme & add energy graph to match chi^2 curve

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 # ab-testing-special-topics
-The simulations used to give intuition and understanding into the reasoning behind why the normal and chi^2 curves are declarative for AB tests.. 
+The simulations used to give intuition and understanding into the reasoning behind why the normal and chi^2 curves are declarative for AB tests through an example of the random walk and random speed problems.
+
+## Random Walk
+Notice how the random walks frequency graph created a normal distribution, which became "more normal" with more points on the walk. 
+This frequency plot represents the (un-normalized) pdf of finding a points, so we can quanitivaly define how probable it is to find a walk at a certain distance.
+
+Relating to AB testing, we can view the t-score as this particle doing a "random walk", with the p-value as the probability of finding a walk at that distance. By converting the average to a t-score, you have effectively normalized the walk, and can use the normal distribution to find the p-value.
+
+When you argue that "if the p-value is less than 0.05, then the null hypothesis is rejected", you are saying that "if the probability of finding a sample in this position is less than .05 and I found it (in your sampleA vs sampleB calculations), then it's highly unlinkely this path is a coicidence and the null hypothesis can be rejected." 
+
+## Random Speeds
+Notice how the distribution of random speeds and enegeries frequency graph is not normal - it's mostly normal but skewed with a longer right tail. This is because speed has no direction (as it's the magnitude of velocity), so the distrubtion is no longer normal.
+
+While the velocity for each dimension in our system (x, y, z) has a normal distribution, the sum of the squares of them results in this non-symmetic, non-normal frequncy map, the chi distribution (not squared yet). Now chi^2 relates the energies of the system (speed^2), which is directly proportional the generalized chaos in the system (entropy). 
+
+Chi^2 is used to test the null hypothesis of "no difference" between categorical variables in AB testing because it measures generalized, non-directional chaos among all dimensions of the system. If your distrubtions from the dimensions are similar, it should converge to be highly-chaotic & high-energy, as stated by the second law of thermodynamics. By contrast, if your underlying distrubtions create an immensely low-chaotic (i.e. low-energy state), then it's highly likely these underlying distrubtions are different. 
+
+Relating to AB testing, when you argue that, for chi^2, "if the p-value is less than 0.05, then the null hypothesis is rejected", you are saying that "if the probability of finding these directions at energy level this low and I found it (in your sampleA vs sampleB calculations), then it's highly unlinkely this state is a coicidence (violates the second law of thermodynamics) and the null hypothesis can be rejected (i.e. these distributions are not the same)." 
+
+In theory, for performing a hypothesis test with categorical variables, we take each dimension to be the difference between the normal distrubtions (of differences in observed-expected) of the samples. This encapsulates the difference between the distrubtions into a normal curve, which we combine into the chi^2 curve (visuals helps this explanation, see video).
+
+## Video of Special Topic Hour
+TODO: add video after the hours
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