Final answer:
The question pertains to the calculation of various probabilities and frequencies associated with rolling two six-sided dice multiple times, applying principles of probability and statistics.
Step-by-step explanation:
The question revolves around the concept of probability in the context of rolling two six-sided dice multiple times and analyzing different aspects such as the probability of rolling doubles, the frequency of rolling a specific number, the cumulative sum of dice rolls, and the probability distribution of rolling two dice. In order to solve these problems, one needs to apply the fundamental principles of probability and statistics.
For instance, the probability of rolling doubles (same number on both dice) with two six-sided dice is 1/6, since there are 6 possible doubles out of 36 outcomes. The frequency of rolling any specific number on one die is expected to be 1/6 multiplied by the number of rolls; in this case, if you roll a die 100 times, you would expect to roll a specific number approximately 16.67 times (100/6).
The cumulative sum of dice rolls involves adding the values of the dice for each roll. The expected cumulative sum after multiple rolls would be the average sum multiplied by the number of rolls. The average sum for two dice is 7, so over 100 rolls, one might expect a cumulative sum around 700.
Finally, the probability distribution for rolling two dice is a list of probabilities for obtaining each possible sum (2 through to 12). This distribution is not uniform because different sums have a different number of combinations to achieve them.