Downloadable - About University

86 Introduction to probability
that the completion time will fall within this interval is 0.2. A summary
of the probability distribution is shown below.
Project completion time Probability
10 to under 14 weeks 0.2
14 to under 18 weeks 0.5
18 to under 22 weeks 0.3
When eliciting a probability distribution it is sometimes easier to think
in terms of the probability of a variable having a value less than a
particular figure. For example, ‘what is the probability that our market
share in a year’s time will be less than 10%?’ This can be facilitated
by deriving the cumulative distribution function (cdf), which gives the
probability that a variable will have a value less than a particular value.
The cdf for the above project is shown in Figure 4.4. It can be seen
that there is a 0.2 probability that the completion time will be less than
14 weeks, a 0.7 probability that it will be less than 18 weeks and it is
certain that the time will be less than 22 weeks.
Sometimes it is useful to use continuous distributions as approximations
for discrete distributions and vice versa. For example, when a
discrete variable can assume a large number of possible values it may be
p(completion time is less than stated value)
1.0
0.8
0.6
0.4
0.2
0
Cumulative distribution
function (cdf)
1.0
10 14 18 22
Time to complete project (weeks)
Figure 4.4 – Cumulative distribution function for project completion time