A fair die is rolled twice with the two rolls being independent of each other. Let M be the maximum of the two rolls and D be the value of the first roll minus the value of the second roll. Are M and D independent?
2 answers
No, there will be a correlation between M and D. As one is large, the other will be large.
If M is 6, the difference can take on values of -5 to +5, with equal probability for each
If M is 1, the only allowed difference is 0. (snakeyes)
The mean of the D distribution (zero) is independent of M, but the standard deviation of D is not.
If M is 1, the only allowed difference is 0. (snakeyes)
The mean of the D distribution (zero) is independent of M, but the standard deviation of D is not.
0 answers