Problem #1
(a)
Likelihood function
L(x1, x2, .., xn, theta) = Product(i = 1,2,..n)f(x, theta) 
			 = Product(i = 1,2,.,n) (theta / (x_i^(theta+1))

Take Logarithm on both sides and partially differentiate this with 
respect to theta and set it equal to zero, 
you will get
			theta = n / (sum(i = 1,2,.,n)ln(x_i))

For the 6 values given in the problem, theta = 0.397
------

(b) H = 0.2V ==> V = 5H

absolute(dV/dH) = |Jacobian| =5

Cv = 0.15 = sigma_v / mu_v; mu_v = 80  (given in the problem)
Using equations 4-22, 
theta_v = 4.37 and omega_v = 0.15

V ~ log Normal (theta_, omega_v)

Using the  Method to obtain the PDF of function of random variable
(Equation 5-41)
you can find the PDF of H
f(h) ~ log Normal(theta_v - ln(5); omega_v) = log Normal(2.761, 0.15)
--------------
(c) The height of the dike for a 5% risk is the value such that
area under the pdf f(h) below that value is 0.95

To get this value 
qlnorm(0.95, 2.761, 0.15) = 20.24ft

------------