R*****n
发帖数: 8658 | 1 X's density is:
f(x)=(1/sqrt(2pi)*sigma*x)*exp(-(log(x)-mu)^2/(2*sigma^2)),x from 0 to infinity
pay attention to the variance of log(x) should be sigma^2.
E(X)=exp(mu+sigma^2/2)
VAR(X)=exp(2(mu+sigma^2))-exp(2*mu+sigma^2)
E(X^n)=exp(n*mu+n^2*sigma^2/2) | n**t
发帖数: 10 | 2 如果X 的概率密度为 f(x)
Y 的概率密度为 g(y)
X 与 Y 为一一对应, 有
g(y) = f(x(y))abs(dx(y)/dy)
in you case, X=log(x),
Y=x |
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