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74 HANDBOOK OF PORTFOLIO MATHEMATICS
FIGURE 2.20 Probability density functions for the Binomial Distribution
(N=5, P=.5)The cumulative density function for the Binomial is:N(X)=
∑X
J= 0(N!/(J!∗(N−J)!))∗PJ∗Q(N−J) (2.35)
where: N=The number of trials.
X=The number of successes.
P=The probability of a success on a single trial.
Q= 1 −P.Figures 2.20 and 2.21 illustrate the probability density and cumulative prob-
ability (i.e., cdf), respectively, of the Bionomial Distribution.
The Binomial is also a discrete distribution. Other properties of the
Binomial Distribution are:Mean=N∗P (2.36)
Variance=N∗P∗Q (2.37)