# Conditional Probability Mass Function The random variable X is Bernoulli(p) with X=1 Px[x] = { P. 1 p, X=0. If X = 1

53 Conditional Probability Mass Function The random variable X is Bernoulli(p) with X=1 Px[x] = { P. 1 p, X=0. If X = 1, a point is selected at random from region A (A is the right-hand side shaded region), and if X = 0, a point is selected at random from region B (B is the left side shaded region), as shown in Figure 2 . If the random point is selected in an upper quadrant, we set Y = 1, and if the random point is selected in a lower quadrant, we set Y = 0. Answer items (a) and (b) assuming that the probability of a point falling inside a region is directly proportional to the area of that region. Note that the contour lines of the shaded regions follows quadratic equations. (a) Find the conditional probability mass function Pyx[Y = y X = x) for x = 0, 1 and y = 0, 1. (b) Find the Py[Y = 0). 3 1 u 0 -4 13 -2 1 1 2 3 4 B A Figure 2 Regions A and B (shaded only).

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