To be formal and reveal relics of a primeval mathematical training:
take random variables in and consider special Borel set :
It has probability with .
Now, in some cases, we can differentiate and so write:
where is called the probability density.
One can clearly interpret as the probability that
random variable x takes values in range x to x+dx.
Consider examples:
(a) In the case of tossed coin, let heads be x=1 and
tails x=0. Then for (an unbiased) coin