PUMaC 2013 · 团队赛 · 第 9 题
PUMaC 2013 — Team Round — Problem 9
题目详情
- If two distinct integers from 1 to 50 inclusive are chosen at random, what is the expected value of their product? Note: The expectation is defined as the sum of the products of probability and value, i.e., the expected value of a coin flip that gives you 5 if tail is 1 1 × 5 = $7 . 5. 2 2
解析
- If two distinct integers from 1 to 50 inclusive are chosen at random, what is the expected value of their product? Note: The expectation is defined as the sum of the products of probability and value, i.e., the expected value of a coin flip that gives you 5 if tail is 1 1 × 5 = $7 . 5. 2 2 SOLUTION: 49 50 ∑ ∑ ij i =1 j = i +1 49 ∑ i ( i + 51)(50 − i ) = 2 i =1 ( ) 49 ∑ 1 1 3 2 = − i − i + 1275 i 2 2 i =1 2 2