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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?

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(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!

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  • $\begingroup$ The theoretical distribution is binomial with rate of success $1/3$ and number of trials $6$. It is usually denoted by $\text{Binomial}(1/3, 6)$. The mean is $2$ and the variance is $ 4/3$. $\endgroup$ – Tunococ Oct 19 '14 at 3:58
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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.

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