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72 HANDBOOK OF PORTFOLIO MATHEMATICS
FIGURE 2.18 Probability density functions for the Binomial Distribution (P=.5)articles, success or failure, hit or miss, and so on. Hence, we say that the
Bernoulli Distribution is adiscrete distribution(as opposed to being a
continuous distribution). The distribution is completely described by one
parameter, P, which is the probability of the first event occurring. The vari-
ance in the Bernoulli is:Variance=P∗Q (2.31)where:Q=P− 1 (2.32)Figure 2.18 and 2.19 illustrate the probability density and cumulative prob-
ability (i.e., cdf) respectively of the Bernoulli Distribution.The Binomial Distribution
The Binomial Distribution arises naturally when sampling from a
Bernoulli Distribution. The probability density function, N′(X), of the Bi-
nomial (the probability of X successes in N trials or X defects in N items or