Let $Y_1, Y_2, Y_3, ...$ be i.i.d r.v. with probability distribution $P(Y_i=1)=P(Y_i=-1)=1/2\ \forall i$ and let $c_1, c_2, c_3 ... $ be a sequence of real numbers.
a) If $\sum_{i=1}^{\infty}c_i^2\lt \infty $, find $P(|\sum_{i=1}^{\infty}c_iY_i|<\infty)$.
b) If $\sum_{i=1}^{\infty}c_i^2=\infty $, find $P(|\sum_{i=1}^{\infty}c_iY_i|<\infty)$.
This is a random walk but I am not sure if it classifies as a Markov Chain or a Martingale. I have this doubt due to the sequence of real numbers.
Any hint? Thanks for your help!