想不通答案，希望有高人能够解释下。
An Intermediate Course in Probability，第一章，problem, 14, 15. 先谢谢了

14. Suppose that X ~ Exp(1), let Y be the integer part and Z the fractional
part, that is, let
Y = [X] and Z = X − [X].
Show that Y and Z are independent and find their distributions.

15. Ottar jogs regularly. One day he started his run at 5:31 p.m. and returned
at 5:46 p.m. The following day he started at 5:31 p.m. and returned at
5:47 p.m. His watch shows only hours and minutes (not seconds). What
is the probability that the run the first day lasted longer than the run the
second day?