Acity's bus's delayed time (x) is uniformly distributed between [0,y] where 0 < = y < = 1 and is uniformly disturbed. suppose you observe a delay time x=x.

a) compute the posterior distribution of y given the data observed and find an approximate value of y by calculating e(y | x=x)

b) suppose the first delay you observe is x(1) = 0.5. the next delay is independently drawn by the same distribution (x(2) ~ uniform [0,y]. given what you have observed from the first delay, what is the probability that the second delay will be more than a 0.5 hour delay?