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Monte Carlo Analysis
Basic Statistical Concepts
have a sample space Ω, that is continuous. Probability distributions can be specified by their
probability distribution function, defined as:
for each y in Ω. From this identity we can calculate the probabilities of Y falling within intervals
as:
If the distribution function F Y is differentiable, it is also useful to define the probability density
function of Y as f Y (y) = dF Y /dy, in which case:
and:
It is often convenient to summarize a probability distribution by one or two statistics that
characterize its main features. The most common are expectation and variance. In the case of
continuous random variable with probability density function f Y , the expectation is
and the variance is:
Expectation provides a measure of location, or average value, of the distribution, while the
variance measures the dispersion or spread of the distribution. The standard deviation is defined
as the square root of the variance, providing a measure of variability in the same units as Y.
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Eldo® User's Manual, 15.3