Question 59057
two distinct integer are chosen at random and without replacment from the first six positive integers, compute the expected value of the absolute value of the difference of these two numbers.
THERE ARE 6C2=6*5/2 = 15... COMBINATIONS POSSIBLE EACH WITH SAME PROBABILITY.
THEIR DIFFERENCE IN ABSOLUTE TERMS COULD BE
NUMBER........DIFFERENCE
12.............1
13.............2
14.............3
15.............4
16.............5
23.............1
24.............2
25.............3
26.............4
34.............1
35.............2
36.............3
45.............1
46.............2
56.............1
HENCE EXPECTED VALUE IS = SUM OF EXPECTED DIFFERENCES/TOTAL POSSIBILITIES
35/15 = 7/3