# Convergence radius of random power series

I have a problem with getting how I should interpret the random power series. I am given $$X_n$$ that are i.i.d random variables. Further the random power series,

$$\sum_{n=0}^{\infty} X_{n}z^{n}$$

Based on this should I determine if there are any deterministic (a.s) radius of convergence of the above series for $$P(X_n=1)=P(X_n=-1)=\frac{1}{2}$$?

• Hint: for what realizations of the $X_n$ will the series fail to converge if $|z|\lt 1$? How about when $z=1$? – whuber Dec 12 '18 at 18:53