What is the difference between probability distribution functions and probability density functions?
Probability density function (PDF) of a continuous random
variable is a function
that describes the relative likelihood for this random variable
to occur
at a point in the observation space.
The PDF is the derivative of the probability distribution (also
known as
cummulative distriubution function (CDF)) which described the
enitre range of values
(distrubition) a continuous random variable takes in a
domain.
The CDF is used to determine the probability a continuous random
variable occurs any (measurable) subset of that range.
This is performed by integrating the PDF over some range (i.e.,
taking the area under of CDF curve between two values).
NOTE: Over the entire domain the total area under the CDF curve
is equal to 1.
NOTE: A continuous random variable can take on an infinite
number of values. The probability that it will equal a specific
value is always zero.
eg. Example of CDF of a normal distribution:
If test scores are normal distributed with mean 100 and standard
deviation 10. The probability
a score is between 90 and 110 is:
P( 90 < X < 110 ) = P( X < 110 ) - P( X < 90 )
= 0.84 - 0.16 = 0.68.
ie. AProximately 68%.
