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 $P(X_n=1)=P(X_n=-1)=\frac{1}{2}$?

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

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