Probability
Functions
Random variables do not have deterministic values. In
advance of a random outcome, like the uncertain duration or cost of a work
package, the project team can only estimate the probable values, but the team
will not know for sure what value is taken until the outcome occurs. Of course,
we do not know for sure that the event will happen at all. The event itself can
only be predicted probabilistically.
In the coin toss, the probability of any specific value of H or T happens to be the same: H = 1 or 0 on any specific toss, 1 if heads, else 0, and
similarly for T.
p(H = T = 50 in toss of
100) = 0.5
But equal values may not be the case for all random variables in
all situations.
p(D = 7 in one
roll of two die) = 1/6 = 0.167
p(D = 5 in one
roll of two die) = 1/9 = 0.111
where D = value of the sum
of the two faces of the die on a single roll.
The probability function [7] is the mathematical relationship between a random
variable's value and the probability of obtaining that value. In effect, the
probability function creates a functional relationship between a probability and
an event:
f(X | value) = p(X
= some condition or value)
f(X | a) = p(X =
a), where the "|" is the symbol used to mean "evaluated at" or "given a value of
the number "a". Example: f(H | true) = 0.5 from the coin toss.
Sections
Syndication
