The throwing of a one or two is called a success. The six dice are thrown together 64 times and the frequencies of the throws with 0, 1, 2,..., 6 successes are summed over all six pairs are as follows:
Success: 0 1 2 3 4 5 6
Frequency: 0 4 19 15 17 7 2
(a)What would be the theoretical probability of success and the mean and variance of the above frequency distribution is all the dice were fair?
My friend and I got different answers. I multiplied by the successes from 0,..6, and my friend multiplied by the frequencies.
Who is correct?
(c) Test the hypothesis that the mean and variance have their theoretical mean?
What kind of test would you suggest? 2-sample binomial test and we can approx with Z? And what kind of test for variance? Chi-sqaured?
Thanks!
I believe your solution is the second one, so you are correct. Part (a) of the problem should not have anything to do with the empirical frequencies.
For Part (c), Chi-squared test seems appropriate.