$\displaystyle E(S^{2}) = \frac{1}{n-1} \left{\sum E(X_{i}^{2}) - \frac{1}{n} E \left[ \left(\sum X_{i}\right)^{2}\right] \right}$
Its not parsing.
1. you need [tex] tags rather than "$"s
2. as {} are meta grouping delimiters used by LaTeX if you want to uses
them as parentheses you have to preceed them with "\"
[tex] \displaystyle E(S^{2}) = \frac{1}{n-1} \left\{\sum E(X_{i}^{2}) - \frac{1}{n} E \left[ \left(\sum X_{i}\right)^{2}\right] \right\}[/tex]
produces:
$\displaystyle \displaystyle E(S^{2}) = \frac{1}{n-1} \left\{\sum E(X_{i}^{2}) - \frac{1}{n} E \left[ \left(\sum X_{i}\right)^{2}\right] \right\}$
3. As far as I am aware the \displaystyle is redundant in the LaTeX implemented here.
RonL