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Why use chi-square?
the Chi Square distribution is a mathematical distribution that is used directly or indirectly in many tests of significance. The most common use of the chi square distribution is to test differences among proportions
What happens to the shape of the chi-square distribution as the df value increases?
As the value of k, the degrees of freedom increases, the (chisq - k)/sqrt(2k) approaches the standard normal distribution.
Does use of chi-square demand a random sample?
Well, sort of. The Chi-square distribution is the sampling distribution of the variance. It is derived based on a random sample. A perfect random sample is where any value in the sample has any relationship to any other value. I would say that if the Chi-square distribution is used, then every effort should be made to make the sample as random as possible. I would also say that if the Chi-square distribution is used and the sample is clearly not a random sample, then improper conclusions may be reached.
What was the motivation for introducing the Gamma distribution?
It can be thought of as a generalization of the Chi-square distribution. See the link to a related WikiAnswer question below.
What is the area underneath curve for chi-square distribution?
1. It is a probability distribution function and so the area under the curve must be 1.
