A Level Maths Notes: S1 – Probability Density Functions (pdf) – Continuous 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. The
example below is for a continuous distribution over the interval
0<=x<=3.
Given the pdf we can find
To
evaluate this expression we find
Hence
to
3 dp.
The expression for the variance
is
fundamental in higher mathematics and physics, especially quantum
physics.
These expressions are also useful for any continuous distribution
defined on an interval
