A random variable is multinomial if (a) each independent trial has k possible outcomes, (b) the ith outcome (category) occurs with probability , where and (c) (Law of Total Probability).
A goodness of fit test is a hypothesis test used to ascertain whether a random variable follows a particular distribution. In a goodness of fit test, the hypotheses are
.
Compare the observed frequencies (actual data from the field) with the expected frequencies when is true. If the difference between the observed and expected frequencies is large, reject .
The goodness of fit test is performed using (a) the critical-value method or (b) the p-value method.