(Solved): 2. (50 pts) Rick and Morty were invited to a dice factory as data scientists. Their task is to exam ...

2. (50 pts) Rick and Morty were invited to a dice factory as data scientists. Their task is to examine if the dice are fairly made. They started with a simple measure, mean. However, they came up with different methods for estimating the mean of each die. Rick argued that for each die it should be rolled a surficiently large amount of times, say $n$, and then the arithmetic average is calculated to estimate the mean of this die. On the other hand, Morty argued that the rolling experiment should be done multiple times, say $k$ times, and the die will be rolled $\frac{n}{k}$ times so that the total amount of rolls will be the same as that Rick does, and then the average over the $k$ averages of the experiments is calculated for the estimation. Whose method do you think makes better sense? Or. they will get the same result? Please use your probability theory and statistics knowledge to mathematically argue. (Note that we exclusively concentrate on the point estimation of mean.) please include the use of expectation, the probability of $X$ intersects the probability of Y, and PMF