作者hiei81 (宝贝。永远)
看板IMO_Taiwan
标题[问题] 不等式
时间Wed Feb 16 03:30:02 2005
Find probability density function D of random variable X s.t.
E[X]=0, Var[X]=(sigma)^2 and X<=c for all X, which minimize E[e^tX]
In fact, the answer would be
Prob[X=c]=(sigma)^2/[(sigma)^2+c^2]
Prob[X=-(sigma)^2/c]=c^2/[(sigma)^2+c^2]
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