9.4.1 Distributions and inverse distributions
Let p(x) be a probability density function, so p(x) ≥ 0 for
all x, and for a discrete density function,
while for a continuous density function,
The corresponding cumulative distribution function
is the probability that a randomly (according to the probability being
considered) chosen value is less than or equal to x. This can be
used to find the probability that a randomly chosen value
is between two numbers:
Prob(x < X ≤ y) = P(y) − P(x)
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Given a value h between 0 and 1, the inverse distribution function for a
distribution takes h to the value of x for which
Prob(X ≤ x) = h.