Figure 1 shows Bohr's model for the hydrogen atom (read the figure text). We let (X, Y) denote the position ofthe electron in relation to the atomic nucleus. In quantum mechanics one can never determine (X, Y) exactly, but mustinstead use a probability distribution. We assume that X ? N (0, 1) and Y ? N (0, 1), i.e. normally distributedwith expectation 0 and variance 1, and that X and Y are independent of each other.