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Q: The properties of chi-square distribution

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It is a discrete distribution in which the men and variance have the same value.

The normal distribution can have any real number as mean and any positive number as variance. The mean of the standard normal distribution is 0 and its variance is 1.

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.

Because each phenomenon is made up of many smaller phenomena which are often independent, each of which has a random element associated with it. The sum of such random variations tends towards the Gaussian (normal) distribution. Also, the distribution has well known properties.

The Poisson distribution. The Poisson distribution. The Poisson distribution. The Poisson distribution.

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It is a discrete distribution in which the men and variance have the same value.

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The normal distribution can have any real number as mean and any positive number as variance. The mean of the standard normal distribution is 0 and its variance is 1.

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