In Example 12.2.12, we can actually compute the median of the distribution of the Xi in

In Example 12.2.12, we can actually compute the median θ of the distribution of the Xi in closed form. Calculate the true median, and see how far the simulated value was from the true value. Find the marginal p.d.f. of X by using the law of total probability for random variables (3.6.12) together with Eq. (5.7.10). The c.d.f. and quantile function are then easy to derive.