Especially in the analysis of randomized algorithms, probabilistic bounds play a pivotal role in the proving of probabilistic theorems. This blog aims to be a reference for such key results that will be used in the randomized analyses conducted in upcoming blogs. Foremost, we cover the all-important Markov and Chebyshev
Recently, I just completed my undergraduate Real Analysis course at UC Santa Cruz, and for the course, we were required to write a paper. I chose to write on this fantastic and pleasantly rigorous intersection of Measure Theory and Probability Theory — in particular, continuous sample spaces. The traditional method
Consider a stream of data that we receive, call them where is the element in the stream. Note that we receive every at the time step and that is then no more in our access once we move on to the next time step. Furthermore, we don’t even know the
There are many methods of introducing structure to random variables in Probability Theory, and traditionally we call this structure a property, and one such property is its distribution. Phrases like “coming from this distribution” or “they distribute as such” or “these variables make this distribution” all refer to this property.