Let X and Y be the values of two stocks at the end of a ﬁve year period. X has uniform distribution in the interval (0, 12), while the value of Y is uniformly distributed on the interval (0, x) when X = x. Find:

a. the density of X given that Y = 35;

b. the density of X given that Y = 3 and the conditional mean of X when Y = 3.

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Let us write down the density function p(x,y). We know that x is uniform on [0,12] and that given X=x, Y is uniform on the interval [0,x] so...

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