[商管] [數統] 幾題頗為艱難的題型
1. Let X be a discrete random variable whose range is the
nonnegative integers . Show that
∞
EX = Σ (1-Fx(k)) , where Fx(k) = P(X≦k)
k=0
2. A random variable X is defined by Z = logX, where E(Z)=0
Is E(X) greater than ,less than , or equal to 1 ?
3. Does a distribution exist for which Mx(t)=t/(1-t),|t|＜1,
If yes ,find it ,if no ,prove it ?
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