CIVL 581 Assignment on Bayesian Approach
Ang & Tang, Vol. I, Ch. 8, # 1, 5, 7, 11, 15
Answers:
#1: (a) 0.76; (b) p”(p = 0.10) = 0.01; (c) 0.828; (d) 0.752.
#5: (a) 0.489, 0.511; (b) 0.0306 m Exp[-(m/4)2/2)] + 0.0204 m Exp[-(m/5)2/2)]; (c)
0.09675.
#7: 0.108 Exp(-/12) for 0.5   < 20; 0 elsewhere.
#11: (a) N(65, 4.47); (b) N(61.7, 2.58); (c) 0.0384
#15: 0.514; 0.193.
Extra Problem:
Suppose the maximum water elevation H during a flood may be described by an
exponential distribution as
fH(h) =  e–h
h0
At a given site no measurements have been made on water elevation during
previous floods. However, the inhabitants recall that only two floods have
occurred in recent years, whose elevations are at least 5 feet. Assume flood
elevations to be statistically independent between floods.
(a) Assume there is no other information for estimating . Determine the
distribution of , its mean value and c.o.v. based on the given information.
(b) What is the probability that the next flood will exceed 5 ft.?
(c) After a period of time, three floods have occurred at the given site and the
maximum water elevations were recorded as 3, 4 and 5 feet, respectively.
What is the updated distribution of , its mean value and c.o.v.?
Answers:
(a) 10 e–10 for   0; 0.1; 1
(b) 0.667
(c) (224/3!) 3 e–22 for   0; 0.182; 0.5