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Advanced Math/Time Series and Conditional Probability


randy patton wrote at 2015-07-07 06:19:39
Perhaps this rendition of Bayes' Rule will help. You can always start with the equality from the axioms of set and probability theory

P(B|A)P(A) = P(A|B)P(B)

where B would represent the 4-day streak event and A the 3-day streak. This can be rearranged by dividing by P(A) to get

probability of 4-day given 3-day = P(B|A) = [ P(A|B)P(B) ] / P(A)

As you say in your follow-up, a 4-day streak can only happen if a 3-day streak has already happened, which means P(A|B) = 1, so

P(B|A) = P(B)/P(A)

just as the radio guy said.

As far as the other streaks go, if for example, the probability of an 8-day given a 7-day would have the same form as the 4 and 3-day case above. The probabilities of the longer streaks do in fact go down quickly, but the ratio of consecutive streaks stays the same (the respective probabilities decrease at the same rate).

You comment that, after a 7-day streak, it should be less probable to get an 8-day streak, meaning an up day occurs, than for a down day to occur ("reverting to the mean"). however, if the occurrence of a single up or down day is 50-50 and is independent of what has happened before, then both possibilities have equal probabilities. This whole problem seems to be a rehashing of the well known example of asking what the probability of getting a heads in a fair coin toss after lots of heads have just been tossed in a row. The answer is 1/2 since the coin doesn't know or care what happened before, it will land on heads or tails with equal probability.

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Scott A Wilson


I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?


Experience in the area; I have tutored people in the above areas of mathematics for over two years in I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.

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