All Questions

Suppose that $Y_1...,Y_n$ are independant gamma random variables: $Y_i \sim \Gamma(\alpha_i,\beta_i)$, with density $f_i(t) = \frac{t^{\alpha_i-1} e^{-\frac{x}{\beta}}}{\Gamma(\alpha) \beta^{\alpha}}$....

Let $f\in C^3(\mathbb R)$ with $f>0$ and $$\int f(x)\:{\rm d}x=1$$ $g:=\ln f$ (and assume $g'$ is Lipschitz continuous) $n\in\mathbb N$, $$s(x,y):=\sum_{i=1}^n\left(g(y_i)-g(x_i)\right)$$ and $$h(...

Let $f\in C^3(\mathbb R)$ with $f>0$ and $$\int f(x)\:{\rm d}x=1\tag1$$ $g:=\ln f$ and assume that $g'=\frac{f'}f$ is Lipschitz continuous (note that this implies that $f'(x)\xrightarrow{|x|\to\...