To estimate the integral $I=\int t(x)g(x)dx$ by Monte Carlo, the sum $\hat{I}=N^{-1}\sum$ $t\left(x_i\right)g\left(x_i\right)/p\left(x_i\right)$ is used, where $x_i$ are draws from the importance sampling distribution $p(x)$. Show that plim $\hat{I}=1$.