Let $X_{1}, X_{2}, \ldots$ be a sequence of i.i.d. observations from discrete uniform $(1,2, \ldots, \theta $ distribution for some integer $\theta>1$. a) Show that $2 \bar{X}_{n}-1$ is a consistent estimator of $\theta$. b) Show that $X_{(n)}$ is a consistent estimator of $\theta$. SP.AS. 1146