Question
The third of these statements is equivalent to a measure being countably additive. For 10 points each:
[10m] Identify these three statements that formalize probability theory in terms of properties of measures. They are named for a Soviet mathematician who co-names a test in non-parametric statistics with Nikolai Smirnov.
ANSWER: Kolmogorov axioms [accept Andrey Nikolaevich Kolmogorov; prompt on probability axioms]
[10e] The axioms of probability characterize event spaces as collections of sets called “[this letter]-algebras.” The capital version of this Greek letter is used to denote summation.
ANSWER: sigma [accept sigma-algebra or sigma-field]
[10h] The third Kolmogorov axiom gives the sum of probabilities of mutually exclusive events, but it directly implies this inequality for the sum of probabilities of any countable collection of events. This inequality is a restatement of sub-additivity of the probability measure.
ANSWER: union bound [or Boole’s inequality]
<Other Science>
Summary
| 2024 ACF Regionals @ Berkeley | 01/27/2024 | Y | 3 | 23.33 | 100% | 67% | 67% |
| 2024 ACF Regionals @ Cornell | 01/27/2024 | Y | 3 | 13.33 | 100% | 33% | 0% |
| 2024 ACF Regionals @ JMU | 01/27/2024 | Y | 10 | 12.00 | 80% | 30% | 10% |
| 2024 ACF Regionals @ Minnesota | 01/27/2024 | Y | 2 | 20.00 | 100% | 50% | 50% |
| 2024 ACF Regionals @ Nebraska | 01/27/2024 | Y | 1 | 20.00 | 100% | 100% | 0% |
| 2024 ACF Regionals @ Rutgers | 01/27/2024 | Y | 2 | 15.00 | 100% | 50% | 0% |
| 2024 ACF Regionals @ Imperial | 01/27/2024 | Y | 1 | 20.00 | 100% | 100% | 0% |
Data
| Oxford A | Imperial A | 10 | 10 | 0 | 20 |