Compute $E[X_1 \mid X_2]$; $E[S_n\mid X_1]$; $E[S_n \mid S_{n-1}]$

Question

Let $(X_n)$ i.i.d integrable random variables and $S_n=\sum_{i=1}^n X_i$.

How can I compute $E[X_1 \mid X_2]$; $E[S_n\mid X_1]$; $E[S_n \mid S_{n-1}]$?

Answer 1

1. $X_1$ and $X_2$ are independent;
2. $S_n = X_1 + \sum_{i=2}^n X_i$
3. $S_n = S_{n-1} + X_n$