[Talk] Fluctuations in coin tossing and random walks
This chapter digresses from our main topic, which is taken up again only
in chapter V. Its material has traditionally served as a first orientation
and guide to more advanced theories. Simple methods will soon lead us to
results of far-reaching theoretical and practical importance. We shall
encounter theoretical conclusions which not only are unexpected but
actually come as a shock to intuition and common sense. They will reveal
that commonly accepted notions concerning chance fluctuations are without
foundation and that the implications of the law of large numbers are widely
misconstrued. For example, in various applications it is assumed that
observations on an individual coin-tossing game during a long time interval
will yield the same statistical characteristics as the observation of the
results of a huge number of independent games at one given instant. This is
not so. Indeed, using a currently popular jargon we reach the conclusion
that in a population of normal coins the majority is necessarily maladjusted.
Until recently the material of this chapter used to be treated by analytic
methods and, consequently, the results appeared rather deep. The elementary
method used in the sequel is therefore a good example of the newly discovered
power of combinatorial methods. The results are fairly representative of a
wider class of fluctuation phenomena to be discussed in volume 2.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 118.168.191.205
EngTalk 近期熱門文章
PTT職涯區 即時熱門文章
14
41