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It is a continuous distribution.

Its domain is the positive real numbers.

It is a member of the exponential family of distributions.

It is characterised by one parameter.

It has additive properties in terms of the defining parameter.

Finally, although this is a property of the standard normal distribution, not the chi-square, it explains the importance of the chi-square distribution in hypothesis testing:

If Z1, Z2, ..., Zn are n independent standard Normal variables, then the sum of their squares has a chi-square distribution with n degrees of freedom.

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Q: Properties of Chi-square distribution
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