作者mangogogo (ka)
看板Statistics
标题Re: [问题] mgf
时间Sun Oct 23 19:09:01 2005
※ 引述《esail (我)》之铭言：
: 令φ(t) = logM(t)
: M(t) is the mgf of distribution
: 试问要如何证明φ'(0)=μ
: φ"(0)=σ^2
φ(t) = logM(t)
φ'(t)=M'(t)/M(t)=>φ'(0)=M'(0)/M(0)=μ/1=μ
φ''(t)=M''(t)*M(t)-(M'(t))^2/(M(t))^2
=>φ''(0)=M''(0)*M(0)-(M'(0))^2/(M(0))^2=E[X^2]-(E[X])^2/1=σ^2 proved
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1F：推 esail:谢谢喔～～^^ 10/24 23:21