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.

**Subject Mathematics Probability**