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626 14. Appendix

14.3.2 Percentage Points of the Chi-Square Distribution
The Table 14.3.2 provides the lower 100γ% point for the distribu-
tion for different values of v and γ. See the Figure 14.3.3.

Figure 14.3.3. The Shaded Area Is the Probability γ
Suppose that X has the distribution with some appropriate v. Now, con-
sider the following examples:

Remark 14.3.1 The percentage points of the distribution can be easily
found using the standard normal Table 14.3.1. Observe that

For example, when γ = .95, one has Thus, from the

Table 14.3.1b we find that
In the Chi-square Table 14.3.2, we have
Remark 14.3.2 The percentage points of the distribution can be easily
found using direct integrals of the exponential pdf. From (5.4.16), observe
that