If you happen to position quite a few issues randomly within the unit sq., what's the distribution of the radius of the biggest circle containing no issues? Of the smallest circle containing four issues? Why do Brownian pattern paths have neighborhood maxima yet now not issues of bring up, and the way approximately have they got issues of raise? Given lengthy strings of letters drawn i. i. d. from a finite alphabet, how lengthy is the longest consecutive (resp. non-consecutive) substring showing in either strings? If an imaginary particle plays an easy random stroll at the vertices of a high-dimensional dice, how lengthy does it take to go to each vertex? If a particle strikes below the impression of a possible box and random perturbations of speed, how lengthy does it take to flee from a deep strength good? If autos on a highway circulate with consistent velocity (random from motor vehicle to car), what's the longest stretch of empty highway you'll find in the course of a protracted trip? in case you take a wide i. i. d. pattern from a 2-dimensional rotationally-invariant distribution, what's the greatest over all half-spaces of the deviation among the empirical and real distributions? those questions conceal a large cross-section of theoretical and utilized likelihood. the typical subject is they all care for maxima or min ima, in a few feel.
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