Category Mathematics
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 […]
Empty bins
Suppose that balls, where is a constant, are thrown sequentially to bins, all of which are initially empty. Let be the number of empty bins after we have thrown balls. Clearly, . Let’s see how we can understand this sequence of random variables. When we move from step to we throw a ball. It either falls in an […]
Graph sphericity
The sphericity of a graph is the smallest dimension such that there exists a mapping such that if and only if . The following theorem is due to Frankl and Maehara and is a nice application of random projections. Here, . Theorem [Frankl-Maehara 1988]: Let be a graph with minimum adjacency eigenvalue where and suppose . […]
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