PROBABILITY DENSITY FUNCTION (PDF)

1. Problem: The frequency or number of observations within a cell , f _k , depends upon the total sample size , n.

   In the example, n = 20; however, if n is increased to 100, then values of frequency, f _k , may change.

2. Solution: Normalize frequency by the total sample size n.

   Defines the probability density function (pdf) of the grouped range values X _k :

   

3. Assumes: Each observed sample is independent of others and represents equally likely events.

   Example Problem: n = 20

   Cell, RV X k	Frequency f k	Probability f(X k ) = f k /n
   2	8	0.40
   3	5	0.25
   4	4	0.20
   5	2	0.10
   6	1	0.05
   	20	1.00