# Binomial Probability (Dice)

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!

• 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 $4/3$. – Tunococ Oct 19 '14 at 3:58