= Solution
Use the positive exponent in the PDF. The TeX introduces a minus sign in the numerator while retaining the positive-sign normalizing constant, which would not define the stated <probability distribution>. The <Curie–Weiss model> assigns equal weights to $s$ and $-s$, since $(\sum_js_j)^2$ is unchanged by simultaneous reversal. This <spin inversion symmetry> pairs every configuration with one having the opposite value of $S_i$, so
$$
\boxed{\mathbb ES_i=0,\qquad\mathbb P(S_i=1)=\mathbb P(S_i=-1)=\frac12.}
$$
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