Theoretical distribution of sum of three four-sided dice?

Question

Picture a theoretical distribution of the sums of three dice. Then picture yourself conducting an experiment by rolling the three dice 100 times and recording the outcome of each roll. The results of your experiment is shown below:

Sum --- Relative Frequency
3 ---- 1%
4 --- 4%
5 --- 9%
6 --- 15%
7 ---- 23%
8 --- 18%
9 --- 13%
10 --- 12%
11 --- 4%
12 --- 1%

a) What is the random vaiable in this experiment?
b) Is the population mean and sample mean different? Why?
c) What assumptions are implied by the theoretical distribution for the sum of the three 4-sided dice?

Answer 1

a) The sum
b) Yes, because if you were to only do this test a few times (creating a small sample of values) the results you would get would almost certainly not exactly match the relative frequencies you listed above; it is only when you repeat this experiment many, many times that your frequencies would converge to the theoretical frequencies.
c) The assumption is that if you repeat the experiment a very large number of times, then you would get frequencies that would get closer and closer to the ones you listed above.