ajtj99's Market Pulse

[hooyatodd]

OT stats discussion:

The choice of a binomial is okay, but note that by using it you are assuming that one day’s gains are independent from all the other days’ gains (assumption C on your link)

I think the question you answered was:
Q1) What is the probability that 6 out of 6 days will be up?

I think you wanted to answer:
Q2) Given I’ve already had 5 up days, what is the probability the next day will be up?

A1) 2% (either using binomial or simply 0.52^6)
A2) 52%

Note that since one day’s gains are assumed to be independent of the gains of all other days, A2 would be 52% no matter how long the string of up days that preceded it. Or you could calculate it by P(day 6 up) = P(6 of 6)/P(5 of 5) = 52%

A way to calculate it without assuming independence would be to find all the instances where there was a string of 5 up days and then see how many out of the total succeeded in printing a 6th up day. The only problem is the sample may be too small to say anything useful.

FWIW
Todd