Reminder: For many relatively simple probability questions such as these, you should find that the math and calculations involved are not at all onerous. The trick is recognizing which concepts apply, and therefore which tools (e.g. formulas) are most appropriate for the job. It is equally important to recognize when the tools in your toolbox do NOT apply! This is so that when looking at data in the real world, or if you are looking at someone else's interpretation of data, you recognize when people are not using or interpreting the data appropriately.

problem 1 :-

You ask your graduate student to roll a die 100 times and record the results.

1] What the expected mean a nd standard deviation of the outcome.

2] The die roll experiment is repeated (though with a different graduate student - for some reason your previous student went to work with a different advisor). However in this case, the die is weighted so that a 6 shows up 11% of the time, a 1 shows up 25% of the time, and all remaining numbers show up 16% (each). Now what is the expected mean and sd of 5000 rolls?

3] What would happen if we changed the experiment to 10,000 rolls?