Certain vs Uncertain Relationships

Joe Thorley · 2018-11-17 · 2 minute read

If you place $100 in your bank which charges $5 in fees and issues 1% annual simple interest then after 365 days you will have $96 in your account. We can write this mathematically as

\[y = x - 5 + x \cdot 0.01\]

where \(x\) is our initial bank balance and \(y\) is our final balance

Alternatively if you had placed your $100 on a horse race at odds of 3:1 it is possible that at the end of the race you receive your original stake back plus an additional $300 for a grand total of $400 if your horse wins or $0 if it loses. Assuming you don’t know whether or not the race is fixed then it’s uncertain how much money you will have although the possible states are well defined, ie, $400 vs $0. We can write this mathematically as

\[ y = x \cdot \begin{cases} 4 \text{ if wins}\\ 0 \text{ if loses} \end{cases} \]

In the first instance the relationship is certain in the sense that given the initial amount ($100) you know the final amount ($97). In the second instance the relationship is uncertain in the sense that although you can calculate the possible final amounts ($400 vs $0) you don’t know which will occur.

Statistics can be defined as the branch of science that studies uncertain relationships.