# Thread: Geometric mean of IIDs with uniform distribution [0,1]

1. ## Geometric mean of IIDs with uniform distribution [0,1]

Let $X_1,X_2,\dots,X_n$ be n independent variables, all with the uniform distribution $U(0,1)$. Am I correct in concluding that the geometric mean $G=\sqrt[n]{X_1\cdot{X_2}\cdots{X_n}}$ of these variables has probability density function $f_G(g)$ given by $\frac{n^n}{(n-1)!}\left(-g\ln{g}\right)^{n-1}$ when $0\le{g}\le1$, and zero for g outside that range? I used the uniform product distribution, along with the "change of variable" associated with the nth root function to find this.

--Kevin C.

2. Hello,

Yes, it's correct

,

,

,

,

# if x1,x2...xn are iid uniform (0,1) find distribution of their geometric mean

Click on a term to search for related topics.