An unfair 12sided die X because 18 come up 10 of the time ea

An unfair 12-sided die X (because 1-8 come up 10% of the time each and 9-12 5% each) has mean 5.7 and standard deviation 3.195, and a fair 20-sided die Y has mean 10.5 and standard deviation 5.766. (You can check these if you\'re interested, but use the rounded versions given here.) We roll both dice. Let S be the sum.

The mean of S is  

The standard deviation of S (to three places after the decimal) is   

Let D be the difference Y-X. The mean of D is  .
The standard deviation of D is  .
If we relabel the 20-sided die {103, 203, 303,..., 1903, 2003}, the mean of the number rolled is  .
If we relabel the 20-sided die {103, 203, 303,..., 1903, 2003}, the standard deviation of the number rolled is  .

Solution