Homework Problem 5, Due Wednesday September 23.
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(a) Find the integral of the function 
          f(x,y) = (1+ xy + y^2 + x^4)^0.5
over the interval [0,1]x[0,1], as an expectation, by means of 
simulated uniform random numbers, to a precision of at least
1.e-2 with (approximate) probability at least .99. Give a suitable
confidence interval for your answer.

(b) By simulation, find the probability distribution of the number of
distinct values among 5 independent random integers (drawn uniformly)
from 0:8, with ALL probability mass values SIMULTANEOUSLY correct
within .01, with a probability of at least .98. How large a simulation
did you need in order to achieve this ?

In (a), you are welcome to check your answer by numerical 
integration [using R function "integrate"], and in (b), by
calculating numerically the analytical formulas for the desired
probabilities. Such checks are desirable but not required.