trueacoustics said:
How would you find/estimate the probability of receiving the same utility bill, to the cent, two months in a row. This is a continuous distribution with an infinite amount of solution. However, for practicality, I want to make the distribution more finite. In reality, my bill will probably never exceed 150. I won't be able to tell you the mean or median of the distribution, but a very rough estimate of the interquartile range is $40-80.
Thanks,
Tony
Hey trueacoustics and welcome to the forums.
Although this might seem like a simple question, it isn't.
The thing for this is to figure out how past bills and usage affects your new bill. If you assume that both bills are independent, then the problem is made much easier. If you assume that your past bill only depends on factors that relate to the previous one, it makes things a little more complex, but still manageable.
The point is you need to first figure out what will affect your bill both on any past data as well as things that don't necessarily relate to the data of your past bills.
Here is a good way to think about this: you could take all your bill data for the past two years and draw some kind of graph. That graph might tell you something useful, but it won't tell you the most important things.
For example you might find that for certain months, you need to use more water, more heating and so on. Now you might argue that this would be reflected in the price of your bill at certain points.
But what for example your electricity company introduces off-peak hours where they charge you significantly less for using power in those times? If you know this then you will pick this out but if you were not aware of this fact you wouldn't know what to think.
So the first thing you need to do is firstly think about what affects your power prices. Does the time of year affect it? What about the day of the week? What about where you live? Does any changes in lifestyle have an impact? (You might be away from home some part of the year)
The point I'm trying to make is not to just think of the data for bill prices because that really in the grand scheme of things doesn't tell you much: if you understand how your actions contribute to the final bill you get each month then you will understand more or less how it is calculated on those principles.
But let's just for the moment say that for your example, that each month is modelling by a normal distribution with mean = m and variance = v and each month is independent from the next.
Basically you will have an interval for your bill price so let's say your interval is [b-d,b+d] where d is some kind of noise correction (for your example I'd make it 2 cents) and b is your bill price.
Then using this you need to calculate P(b - d < A < b + d) x P(b - d < B < b + d) which can be found if you standardize the values based on (m,v) and then use a computer.
But I really really have to stress: this is so simplifying that it's probably useless in a practical sense.
It's the same kind of reason that looking purely at stock price history data is dangerous if you want to actually do serious investing especially if you don't understand anything about how markets work, how things are valued, how to assess a business model and how it makes money and so on.
