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Chapter 1: Problem 11

Two distinct integers are chosen at random and without replacement from the first six positive integers. Compute the expected value of the absolute value of the difference of these two numbers.

Short Answer

Expert verified
The expected value of the absolute value of the difference of two randomly selected distinct numbers from the first six positive integers is the sum of the absolute differences divided by the number of pairs, which is 15.

Step by step solution

01

List all possible pairs

Find all possible pairs of distinct numbers from 1 to 6. These are (1,2), (1,3), ..., (1,6), (2,3), ..., (2,6), ..., (5,6). There will be 6 choose 2 = 15 in total.
02

Calculate absolute differences

Calculate the absolute value of the difference of each pair. For example, for the pair (1,2), the absolute difference is |1-2| = 1. Do this for all pairs.
03

Find the average

Sum up all the absolute differences from step 2 and divide by the total number of pairs (i.e., 15). This is the expected value.

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