Four line graphs.

In each graph the horzontal axis shows chi-squared with a specified number of degrees of freedom, 1, 3, 6, or 15, and is numbered 0, 10, 20, 30. The vertical axis is labeled "Probability density" and numbered 0. 0.1, 0.2, and 0.3.

The graph for one degree of freedom starts at chi-squared just above zero and probability density about 0.28. It descends very rapidly, becoming less steep and merging with the horizontal axis at chi-squared = 7. The distribution is very highly positively skew.

The graph for three degrees of freedom starts at chi-squared = zero and probability density = zero. It rises very steeply to a mode at chi-squared = 2 and probability density = 2.4. It then descends very rapidly, becoming less steep and merging with the horizontal axis at chi-squared = 12. The distribution is highly positively skew.

The graph for six degrees of freedom starts at chi-squared = zero and probability density = zero. It rises to a mode at chi-squared = 4 and probability density = 1.3. It then descends fairly gently, becoming less steep and merging with the horizontal axis at chi-squared = 22. The distribution is positively skew.

The graph for fifteen degrees of freedom starts at chi-squared = 2 and probability density = zero. It rises to a mode at chi-squared = 12 and probability density = 1.3. It then descends fairly gently, becoming less steep and merging with the horizontal axis at chi-squared = 22. The distribution is slightly positively skew.

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This page maintained by Martin Bland.

Last updated: 27 July, 2007.