. A CAS can expand
h
=
h
(t) and list the respective probabilities,
P
(
X
=
x
), the coefficients of
i
n the expansion.
SolutionDiscrete Distribution Exa mple
There are times when an infinite series must be evaluated. Some of these problems are easy to solve and others are more challenging. Sometimes it is better to do a problem "by hand" rather than use the computer.
The power of the probability-generating function (factorial moment-generating function) for determining a p.d.f. can be illustrated with a very simple problem. Let
X
equal the number of times that an
n
-sided die must be rolled to observe each face at least once. The probability-generating function of
X
, as a function of
t
, is
. A CAS can expand
h
=
h
(t) and list the respective probabilities,
P
(
X
=
x
), the coefficients of
i
n the expansion.
Solution