
A histogram based on the first and third columns of the complete table is shown in the left graph of
Figure 5.109. The empi rical probability density function
^
f
z
(u) is obtained by connecting the points
(
z
i
, n
i
) and rescaling the ordinate values to f
i
using Equation 5.133 to make the area under the resulting
curve equal to 1.
f
i
¼
n
i
Number of trials width of interval
¼
n
i
100,000 0:005
¼
n
i
500
(5:133)
Finally, a data point is added at
z
i
¼ 0:6050, f
i
¼ 0 to assure the pdf
^
f
z
(u) returns to zero at the
upper tail. The result is shown in the right graph of Figure 5.109.
The theoretical probability of z falling in a certain interval is the area under f
z
(u) for ...