Let $\underline{Y}:=\left( Y_1,...,Y_n\right)$ be a vector with stochastic independent, identically distrubuted random variables with values in $\left\{1,2,3,...\right\}$ . For a permutation $\sigma \in S_n$ , denote $T_{\sigma}: \mathbb{R}^n \rightarrow \mathbb{R}^n $ of the coordinates, so $T_{\sigma}(y_1,...,y_n):=(y_{\sigma}(1),...,y_{\sigma}(n))$
a)Show for all $\sigma \in S_n$ the distribution of $\mathbb{P}Y \circ T{\sigma}^{-1}$ is equal.
b) Argue that for every $1\leq i, j\leq n$ applies:
$\mathbb{E}\left(\frac{Y_i}{\sum_{i=1}^n Y_i}\right)= \mathbb{E}\left(\frac{Y_i}{\sum_{i=1}^n Y_j}\right)$
c) Argue that for all $1\leq k \leq n$ applies: $\mathbb{E}\left(\frac{\sum_{i=1}^k Y_i}{\sum_{i=1}^n Y_i} \right)= \frac{k}{n}$
can someone please give me a tip for starting ?