Imagine there are six cards with values from 1 to 6. Three cards are chosen at random, each card having an equal probability of being chosen, and their values are added together.
What will the average sum be? And what is the standard deviation?
I know how to calculate these quantities when it is possible to repeat the values, but how to calculate in this case when a value can only fall once? In the first choice of cards, all have the same probability of being chosen. However, what happens later when one of them is chosen and can no longer be chosen? Does this influence the mean sum and standard deviation account?