A source transmits symbol \( S \) that takes values uniformly at random from the set \( \{-2, 0, 2\} \). The receiver obtains \( Y = S + N \), where \( N \) is a zero-mean Gaussian random variable independent of \( S \). The receiver uses the maximum likelihood decoder to estimate the transmitted symbol \( S \).
Suppose the probability of symbol estimation error \( P_e \) is expressed as follows:
\[
P_e = \alpha P(N>1),
\]
where \( P(N>1) \) denotes the probability that \( N \) exceeds 1.
What is the value of \( \alpha \)?