Dear Students,
just two parting thoughts for today's lecture:
1) As we said, let me re-emphasize that the main "bang for the buck" you get out of today's lecture is the techniques we developed and analyzed.
2) To add a bit of intuition around uniformity testing, an important intuition concerns symbols that we see multiple times. We have done the calculation and seen that under the uniform distribution, this is very rare. You can do a side calculation to see that under non-uniform distributions, repeated symbols become considerably less rare. Now, you can see that the test statistic we analyzed together, thanks to the squaring, will give a lot of weight to symbols that we see multiple times.
Have a nice evening!
