Most spreadsheet models compute one or more output values that
depend on one or more input variables. The notation defines
n inputs, m outputs and m functions
relating the input variables to the output values.
The values for the inputs are placed in cells on the worksheet
and the values for the outputs appear in other cells. The spreadsheet
model converts the inputs to the outputs using formulas on the
worksheet or perhaps algorithms implemented in VBA. We consider
here situations in which at least one of the inputs is not known
with certainty. Although it may be that the analyst has no idea
what values an input might take, it is often useful to assume
that its value follows a known probability distribution. Then
we can say that the input is a random variable and use probability
theory to make statements about the outputs. That is the purpose
of the Function and associated Moments features
of the Random Variables add-in.
When some collection of inputs are defined as random variables
with specified distributions, we want to be able to compute
moments of the output values, specifically the mean and variance.
Two methods are provided, enumeration and Monte
Carlo simulation. When the random variables are discrete,
enumeration generates all possible values of the random variables
and uses probability theory to compute exact values of the moments.
When the random variables are continuous, the enumeration method
provides only approximate results.
Monte Carlo simulation samples the probability space by randomly
drawing values for each input variable. Using the samples, the
method estimates the moments using simple statistics.
Later, we allow some of the variables to be set by an optimization
method such as linear programming. With this capability we can
begin to discuss some issues related to Stochastic Programming.
There are several pages describing the Functions command.
Click a link at the left to review them.