Solved and Unsolved Problems

[摘要] The column this month is devoted to probability theory. The proposed problems range from basic to fairly demanding so a widerange of our readers should be able to tackle them. As always, thereis also a proposed open research problem. The open problem, alongwith the relevant discussion, is provided by Martin Hairer.Probability theory traces back to the 16th century, when the Italian polymath Gerolamo Cardano attempted to mathematically analyse games of chance. More specifically, his book about games ofchance, published in 1663 (written ca. 1564), contains the first systematic treatqment of probability. Probability theory also traces backto 17th century France, when Blaise Pascal and Pierre de Fermatcorresponded about problems of games of chance. In modern mathematics, probability theory is an extremely applicable and versatilefield, which is used in a surprisingly broad spectrum of areas, such asweather prediction, medicine/biology, equity trading, machine perception, music, etc.