Explain how to simulate a random two-dimensional vector x with a joint pdf f_x(x) that is uniformly distributed in the shaded region. Assume that you have access to independent samples from a uniform distribution in [0, 1]. Explain your method, justifying why it works. Then implement it in a code along with a scatterplot of 1,000 samples.

0.8 0.6 0.4 0.2 C 0 0.25 0.5 0.75