Difference between revisions of "2022 SSMO Accuracy Round Problems/Problem 1"
(Created page with "==Problem== Consider a bijective function (meaning each element in the domain maps to a distinct element in the range) <math>f:S\rightarrow S,</math> where <math>S=\{1, 2, 3,...") |
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| + | By linearity of expectation, we can take <math>f(1),f(2),f(3)</math> separately. The average of <math>f(x)</math> is clearly <math>3</math>, so the average of <math>f(1)+f(2)+f(3)=3+3+3=\boxed{9}</math>. | ||
| + | |||
| + | ~ [https://artofproblemsolving.com/wiki/index.php/User:Eevee9406 eevee9406] | ||
Latest revision as of 21:50, 19 March 2025
Problem
Consider a bijective function (meaning each element in the domain maps to a distinct element in the range) 
where 
. What is the average of 
, over all 
?
Solution
By linearity of expectation, we can take 
separately. The average of 
is clearly 
, so the average of 
.
