关于一个猜想的巧证

The Skillful Proofs on the Conjecture

文章分别利用母函数和随机变量的和式分解不仅巧妙地证明了一个猜想———在独立重复试验中,某事件发生的概率是p,则第m次事件发生所需的试验次数ξ的数学期望为mp,而且还得到了ξ的方差为m(1-p)p2.

The conjecture, which if the probability of an event is p then the expectation of the experiment times ξ where the event exactly occurred the mth m/p in a sequence of independent trials ,is respectively proved skillfully by probability generating function and decomposed sum formula, Furthermore,it is proved that the variance of the ξ is m（1-p）/p^2