After all students have left the classroom a statistics prof

After all students have left the classroom, a statistics professor notices that four copies of the text were left under desks. As the beginning of the next lecture, the professor distributes the four books in a completely random fashion to each of the four students (1, 2, 3, and 4) who claim to have left books. One possible outcome is that 1 receives 2’s book, 2 receives 4’s book, 3 receives his or her own book, and 4 receives 1’s book. This outcome can be abbreviated as (2, 4, 3, 1).

Solution

miu = 2+4+3+1 / 4 = 2.5

sigma

(2 - 2.5)^2 + (4 - 2.5)^2 + (3 - 2.5)^2+ (1 - 2.5)^2

0.25 + 2.25 + 0.25 + 2.25 = 5

sigma = 5 - 2.5/4 = 4.375