A
Level Maths Notes: S1 – Probability Density Functions (pdf) –
Discrete Distributions
Every probability distribution has a probability density function,
in terms of which it is usually defined. The probability density
function for the normal distribution is
for
the uniform distribution it is
for
values between
and
and
zero outside this interval. Both of these examples are continuous
distributions, where any value in an interval may occur, though there
are many examples of normal and uniform discrete distributions. Some
distributions are defined by the values they take over an interval,
either one by one in the case of a discrete distribution, or in terms
of a function, for either continuous or discrete distributions. For
example:
Given the pdf we can find
To
evaluate this expression we find
Hence
The expression for the variance
is
fundamental in higher mathematics and physics, especially quantum
physics.
