What is the conditional expectation of: $$\mathbb{E}\left[(X_1+X_2)^{10}\mid X_1\right]$$ with $X_i$ i.i.d: $P(X_i=1)=0.5=P(X_i=-1)$, for $i=1,2$.
How do I need to start this? I guess, I need to rewrite $(X_1+X_2)^{10}$? And eventually take out what is known, which is the $X_1$. Can someone help on how to start with this?