What if I find a 1963 quarter? Or a 1962 quarter? I could integrate the probability function over all ages from infinity to 1964 - or I could just do it as a super simple python program.įor years up to age 60, this gives a probability of 0.337 to find a coin that is from 1964 or earlier. This means that of all coins, there is a 0.029 chance of finding a 1964 quarter.īut wait. From my coin data above, 0.7273 of all coins are pre-1999. Of course, this assumes all of my quarters are before 1999. I would just put in an age of 34 (remember, this is measured from the year 1998). From this, I can get a probability of finding a 1964 quarter. Here P is the probability and t is the age of the coins in years. Can I use this to get a probability distribution for different years? Of course I can, but will it be any good? Let me use the pennies and nickels as an example of a non-looted sample of coins. This might be sort of a stretch in terms of modeling, but here's what I'm going to do. Suppose that no one even knew that older quarters and dimes were mostly silver such that they would still be in circulation. I suspect that they take these older coins out of circulation when they find them. Yes, by "people" I mean both normal humans and other things like banks and the US government. What does this tell me? It tells me that if people weren't hoarding the silver coins, I should expect to find at least a few silver quarters and dimes. You can see from the data (especially since the graph is on Plotly) that there are about the same number nickels and pennies from 1960-64 and from 64-70.
Maybe that isn't crazy, but just surprising (and cool). What's crazy about this? I found TWO 1911 pennies.