[問題] 幾題艱難的數理統計
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 ?
感謝各位統計高手的協助,祝各位事業進步,學業順利!
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