作者magicyung (magic)
看板Statistics
標題[問題] 關於指數常態分配
時間Sun Mar 12 22:49:42 2006
有請機率模型高手
A random variable X is said to be lognormally distribution
with mean u and σ^2 ， if Y=lnX is normally distribution with
mean u and standard deviation σ
1.Derive the rth moment of X
2.Find P(X >= x)
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◆ From: 218.184.119.35
1F：推 szuyuancheng:E(X)=E(e^Y)=exp(u+0.5*σ^2) 03/12 23:39
2F：→ szuyuancheng:E(X^2)=E(e^2*Y)=exp(2*u+0.5*(2*σ)^2) 03/12 23:41
3F：→ szuyuancheng:E(X^2)=E(e^(2*Y))=exp(2*u+0.5*(2*σ)^2) ↑更正 03/12 23:44
4F：→ szuyuancheng:E(X^r)=E(e^(r*Y))=exp(r*u+0.5*(r*σ)^2) 03/12 23:47
5F：推 szuyuancheng:P(X≧x)=Q(z) where z=(lnx-u)/σ 03/13 00:53