= Solution
For the standard <Cauchy distribution> tail, use the indicator
$$
\boxed{\theta(x)=\mathbf1_{\{x\geq k\}}.}
$$
Then $\int\theta(x)f(x)\,dx$ is the desired <probability>, and the ordinary <importance sampling> estimator is $n^{-1}\sum_i f(x_i)\mathbf1_{\{x_i\geq k\}}/g(x_i)$. The proposal must cover the nonzero integrand, namely the upper tail. A proposal restricted to $[0,k]$ cannot directly estimate this indicator <integral>; part (v) instead uses a complementary bounded-interval identity.
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