A **density** is a continuous
non-negative function defined on all the reals
and such its integral is equal to 1.

For *B*=[*a*,*b*] an interval:

If we take *b*=*a*, we see that for all
*a*, the probability that
a continuous random
variable takes on that value
is 0, this is the big difference
with discrete random variables.

This implies:

Intuitively for a very small width
the probability
will be proportional to
the density at *x*: