# Statistics Problems and Probability

Wednesday December 15, 2021

and variance of the frequency distribution if all the dice were fair? (b) What is the empirical probability of success calculated from the data, and what ls the sample average and vruiance’l (e) Test the hypotheses that the mean and variance have their theoretical values. (d) Calculate the expected frequencies in the seven cells of the table on the assumption that the probability of success is exactly !· (e) Make a chi-square test of agreement of the observed with the expectcd frequencies (combining the frequencies for zero and one successes and also for five and six successcs so that the expectcd frequency within each cell is greater than 5). The numbe.r of degrees of freedom for the test is the number of frequencies compared /ess 1, since thc total of the expected frequencies has been chosen lo nmtch the actual total number of trials

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