# The following code was provided by Nuño Sempere, it comes directly from the post https://www.lesswrong.com/s/rDe8QE5NvXcZYzgZ3/p/j8o6sgRerE3tqNWdj
## Initial setup
yearly_probability_max = 0.95
yearly_probability_min = 0.66
period_probability_function(epsilon, yearly_probability) = 1 - (1 - yearly_probability) ^ (1 / epsilon)
probability_decayed(t, time_periods, period_probability) = 1 - (1 - period_probability) ^ (time_periods - t)

## Monthly decomposition
months_in_a_year=12

monthly_probability_min = period_probability_function(months_in_a_year, yearly_probability_min)
monthly_probability_max = period_probability_function(months_in_a_year, yearly_probability_max)

probability_decayed_monthly_min(t) = probability_decayed(t, months_in_a_year, monthly_probability_min)
probability_decayed_monthly_max(t) = probability_decayed(t, months_in_a_year, monthly_probability_max)
probability_decayed_monthly(t) = probability_decayed_monthly_min(t) to probability_decayed_monthly_max(t)

probability_decayed_monthly
## probability_decayed_monthly(6)
## mean(probability_decayed_monthly(6))