Proposed Problem: Zeros of a Random Power Series

A random power series f(t) = sum from n=0 to inf eta sub n t sup n, where the the eta sub i are independent random variables taking the values {+1, -1} with equal probability, has infinitely many zeros on the interval (0,1) with probability one. some remarks are made on the number of zeros of f(z) in the interval I sub u = [0,1 -u], as u -> 0.