What is the difference between probability distribution functions and probability density functions?

Answer 1

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%.