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Pb. 3.21 Assume that you have two dices (die), one red and the other blue.
Tabulate all possible outcomes that you can obtain by throwing these die
together. Now assume that all you care about is the sum of spots on the two
die. Find the entropy of the outcome.

Homework Problem

Pb. 3.22 A so-called A-law compander (compressor followed by an
expander) uses a compressor that relates output to input voltages by:

y =± Ax for x ≤ 1 / A
1 + log( A)

1 + log( Ax) 1
y =± for ≤ x ≤ 1
1 + log( A) A

Here, the + sign applies when x is positive and the – sign when x is negative.
x = v /V and y = v /V, where v and v are the input and output voltages. The
i o i o
range of allowable voltages is –V to V. The parameter A determines the
degree of compression.
For a value of A = 87.6, plot y vs. x in the interval [–1, 1].

3.7 Examples with the Exponential Function
Take a few minutes to review the section on the exponential function in the
Supplement before proceeding further.

(Recall that exp(1) = e.)

In-Class Exercises
2
13
9
5
Pb. 3.23 Plot the function y(x) = (x + x + x + x + 1) exp(–4x) over the inter-
val [0,10].
Pb. 3.24 Plot the function y(x) = cos(5x) exp(–x/2)) over the interval [0, 10].
Pb. 3.25 From the results of Pbs. 3.23 and 3.24, what can you deduce about
the behavior of a function at infinity if one of its factors is an exponentially
decreasing function of x, while the other factor is a polynomial or trigonomet-

© 2001 by CRC Press LLC