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Expected values 87
easier to treat it as a continuous variable. In practice, monetary values
can usually be regarded as continuous because of the very large number
of values which can be assumed within a specified range (consider,
for example, the possible revenues in the range $0 to $1 million which
could be earned by a company). This might also apply to the sales of a
product. For example, the number of tins of baked beans sold must be
an integer, but if sales can range from 0 to 5 million tins then, again, the
uncertain quantity can take on a very large number of possible values.
Similarly, it is often convenient to use discrete distributions as approximations
to continuous distributions, particularly when constructing
decision tree models (see Chapter 6). For example, we might approximate
the continuous distribution of project completion times above by
using the midpoints of the three intervals to obtain the following discrete
distribution:
Expected values
Project completion time Probability
12 weeks 0.2
16 weeks 0.5
20 weeks 0.3
Suppose that a retailer runs a small shop selling television sets. The number
of color sets she sells per week follows the probability distribution
shown below:
1.0
No. of sets sold Probability
0 0.01
1 0.10
2 0.40
3 0.30
4 0.10
5 0.09
1.00
If this probability distribution applies to all weeks (e.g. we will assume
there is no trend or seasonal pattern in her sales) then we might be