Question 59057: please help me in this
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.
Found 2 solutions by stanbon, venugopalramana:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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Some problems you just have to do by brute force.
List the numbers 1 to 6
Form all possible pairs with repeating in any pair:
1,2;1,3;1,4;1,5;1,6
2,3;2,4; etc.
Near each pair put the abolute value of the difference for each pair.
1;2;3;4;5
1;2;3;4
1;2;3
1;2
1
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There are 15 differences
P(1)=5/15
P(2)=4/15
P(3)=3/15
P(4)=2/15
P(5)=1/15
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You know how to calculate expected value:
1*(5/15)+2*(4/15)+3*(3/15)+4(2/15)+5(1/15)
=35/15=7/3=2 1/3
Cheers,
Stan H.
Answer by venugopalramana(3286)  (Show Source):
You can put this solution on YOUR website! 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
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