Solution
= Solution
For the independent standard normals stipulated in this part, simulate $n$ values and average the exceedance indicators:
$$
\boxed{\widehat z_0=\frac1n\sum_{k=1}^n\mathbf1_{\{X_k>c\}}.}
$$
Each indicator is Bernoulli with <probability> $z_c$, so <expectation> and independence give
$$
\boxed{\mathbb E\widehat z_0=z_c,\qquad v_0=\operatorname{Var}(\widehat z_0)=\frac{z_c(1-z_c)}n.}
$$
Thus the Monte Carlo estimator is unbiased.