18.05 Lecture Notes - Lecture 6: Mit Opencourseware
Document Summary
In this appendix we give more formal mathematical material that is not strictly a part of. This will not be on homework or tests. We give this material to emphasize that in doing mathematics we should be careful to specify our hypotheses completely and give clear deductive arguments to prove our claims. We hope you nd it interesting and illuminating. 2 proof the histogram will probably match the pdf: We stated that one consequence of the law of large numbers is that as the number of samples increases the histogram of the samples has an increasing probability of matching the graph of the underlying pdf or pmf. We prove that here by applying the loln to each bin in the histogram. De ne an indicator (bernoulli) random variable bk for each bin, which is 1 if x is in bin k and 0 otherwise. One proof of the loln follows from the following key inequality.
