# Special Case Probability

Suppose there exists an ideal system in which you have perfect data 100% c.i. This data tells you that the price of gasoline will move a distance (not displacement) of +/- 10% in the next 7 calendar days with a 70% probability.

On day 1 the price of gasoline is $1.00. In the following days from 1-6 the price is in flux and arrives at precisely$1.00 on day 6.

Your data tells you that gasoline will move a distance of +/- 3% in 1 day with 70% probability.

Are both of these probabilities still valid? The 7 day and the 1 day? If yes, is there any edge that can be calculated when these special cases present themselves. Have the 7 day odds changed and is there less than a 70% chance of the +/- 10% move happening in one day? If so, please explain how/why to calculate these changes.

Please explain this at the level of basic statistics, as my education in statistics is not advanced in any way. Thank you.

It is simple enough. The first prediction was valid on the day it was made relevant to a day seven days in the future, and, it is not valid on day six. On day six, a new probability was calculated and the clock was reset. The second prediction is relevant to day six for predicting day seven prices.

Imagine that a prediction is a box containing a Schrödinger's cat. Here we assign a probability of the cat in a box being alive of 70% at day seven and 30% of being dead. Now if you peek into the box at day six, you are no longer looking at a probability, you are then looking at a cat that is either dead or alive. If the cat is still alive, and you reseal the box then you have restarted the clock and the cat now has a better probability of being alive at day seven than it would have had.

In order to calculate what the exact probabilities are, we need to know more information about how prices change from day to day, that is if the price changes are erratic the calculation would be different than if the price changes are more or less the same amount when they occur. For prices, like stock market values, the changes tend to be lognormal distributed.

• Thanks for the answer. Can you help me understand why the probability is still not valid on day 6? Why would the probability of a 7 day movement reset on day 6? Wouldn't the 7 days need to be complete for that probability to be categorized into either part of the 70% that does happen or the 30% that doesn't happen. I assume it must still be possible, but is now far less likely. How much so -- I'd like to calculate it if possible. Aug 19, 2018 at 2:21
• I see. The detail in your answer helps, much appreciated. So in your example using the cat, if it were prices, if the price were closer to the +/- 10% than the probability would obviously be higher and this makes sense, but now for the math -- how do I use said info to calculate the probabilities. Let's assume I have what's required. P(70% in 7 days) = 1 - 0.30 = [P(day 1)+P(day 2)+(P(day 3)+P(day4)+P(day5) + P(day6)+ X] ? I'm no expert in probability study so please bear with my rough notation. Aug 21, 2018 at 5:45
• Need to know how prices change in time to answer. Got data?
– Carl
Aug 21, 2018 at 15:36
• Yes I have data but I need the applicable formula(s) to use it properly. Sep 5, 2018 at 20:33
• The only way to know what formula is applicable is to find the correct formula using the data, that is, no data, no formula.
– Carl
Sep 5, 2018 at 23:09