Category Probability

Expectation of minimum of n i.i.d. uniform random variables

Let  be independent uniform random variables from , and consider the random variable . Computing the expectation is a routine computation: . However, there a slick way of computing this expectation. Let be another uniform random variable in . Consider the probability . On the one hand due to symmetry, it is equal to , on […]

Fair allocation of a pizza

An observation on edge densities of the union of isomorphic copies of a fixed graph

Consider a fixed graph with vertices and edges respectively. Assume that is balanced which means that the maximum edge density among all possible subgraphs of is achieved from $H$. Take two copies of , call them and create a new graph . In case the two copies are edge disjoint then the edge density of […]