Random
Variables and Their Functions in Projects
Random
Variables
So far, we have discussed random events (tails coming up on
a coin toss) and probability spaces (a coin toss can only be heads or tails
because there is nothing else in the probability space), but we have not
formally talked about the numerical value of an event. If the number of heads or
tails is counted, then the count per se is a random
variable, CH for heads and CT for tails. [6] "Random variables" is the term we apply to numerical outcomes of events when the
value cannot be known in advance of the event and where the value is a number
within a range of numbers. When a random
event is completed, like tossing a coin 100 times, then the random variables
will have specific values obtained by counting, measuring, or observing. In the
project world, task durations denoted D
with values in hours, days, or weeks and cost figures denoted C with values in dollars, pesos, or euros are two among
many random variables project managers will encounter.
If a variable is not a random variable, then it is a deterministic
or single-point variable. A deterministic variable has no distribution of values
but rather has one and only one value, and there is no uncertainty (risk) as to
its measure.
As examples of random and deterministic variables, let us say that
we measure cost with variable C and that
C is a random variable with observed
values of $8, $9, $10, $12, and $15. The range of values is therefore from $8 to
$15. We do not know C with certainty,
but we have an expectation that any value of C would be between $8 and $15. If C were deterministic and equal to $13.50, then $13.50 is
the only value C can have. Thus, $13.50
is a risk-free measure of C.
If C were a random
variable with values from $8 to $15, we would also be interested in the
probability of C taking on a value of $8
or $12 or any of the other values. Thus we associate with C not only the range of values but also the probability
that any particular value will occur.
Sections
Syndication
