Question: 14. A point is selected at random and uniformly from the region R = $ (x, y): |x|+|y| 1 % . Find the conditional

14. A point is selected at random and uniformly from the region R = $ (x, y): |x|+|y| ≤ 1 % . Find the conditional probability density function of X given Y = y. 15. Let $ N (t): t ≥ 0 % be a Poisson process. For s < t show that the conditional distribution of N (s) given N (t) = n is binomial with parameters n and p = s/t. Also find the conditional distribution of N (t) given N (s) = k.

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