DeGroot (1986) gives the following example of the Borel Paradox (Miscellanea 4.9.3): Suppose that X1 and X2 are iid exponential(l) random variables, and define Z = (X2 - 1)/X1. The probability-zero sets (Z = 0} and {X2 = 1} seem to be giving us the same information but lead to different conditional distributions.
(a) Find the distribution of X1|Z = 0, and compare it to the distribution of X1|X2 = 1.
(b) For small ϵ > 0 and x1 > 0, x2 > 0, consider the sets

Draw these sets and support the argument that B1 is informative about X1 but B2 is not.
(c) Calculate P(X1

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B = {(z1, z2) : -E < 1=