Biostatistics 615 / 815
Problem Set 7
Due November 17, 2004
Random Number Generation
1.
An old text book on computer simulation recommends the following sequence of
pseudo-random numbers:
I
j+1
=
a I
j
mod
m, with a = 20,403 and m = 2
15
.
What is the period of this random number generator, that is, how many numbers
can be generated before the sequence repeats itself?
2.
Consider the following formula for generating pseudo-random sequences:
I
j+1
= (
a I
j
+
c
) mod
m
When c = 1 and m = 32, examine the resulting sequences when:
a)
a = 13
b)
a = 17
c)
a = 19
d)
a = 10
Which of the three sequences appear random? Do all sequences have a full period
(32 is the maximum period in this case)?
Integration
3.
Implement code to calculate the integral of the function
f(x) = (1 + x)/(1 + x
2
)
in
the interval (2, 4) using each of the following numerical methods:

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