Ralph Vince - Portfolio Mathematics

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ch02 JWBK035-Vince February 12, 2007 6:50 Char Count= 0


Probability Distributions 73

FIGURE 2.19 Cumulative probability function of the Bernoulli Distribution
(P=.5)

X heads in N coin tosses, etc.) is:

N′(X)=(N!/(X!∗(N−X)!))∗PX∗Q(N−X) (2.33)


where: N=The number of trials.
X=The number of successes.
P=The probability of a success on a single trial.
Q= 1 −P.

X!=X∗(X−1)∗(X−2)∗...∗ 1 (2.34)


which can be also written as:

X!=


X∏− 1


J= 0

X−J (2.34a)

Further, by convention:

0!= 1 (2.34b)
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