Tue 7 Oct 2008
Probably A Good Sign?
Posted by admin under Grad School, Mathematics
I only have one course this semester, focusing on my Probability and Random Processes course and doing research. This is by design, since I knew probability is a course I haven’t taken in 6+ years now…and I am super rusty. But I have our text for the class, the schaum’s outline, and 3 other probability and random processes texts, and have been reading like crazy this semester, and doing sample problems out of the 4 texts and schaum’s. Daily. It’s good because I am having a much better time with this material than I expected, although the homeworks have been taking a long time to complete.
All this being said, here’s a sign it’s really starting to mess with my life: when I woke up this morning I asked myself what the probability of me getting out of bed when my snooze alarm went off for a third time (it’s set for 10 min intervals). So I told myself, given how freezing it was in my apartment, and that I didn’t feel particularly awake, that I’d rate the likelihood of me getting out of bed on a given snooze alarm as 2/5, assuming I feel the same way independant of which snooze alarm is going off.
SO to get out of bed at the third snooze would be the probability of 2 failures to get out of bed, again assuming independence to make my just woken life easier, and one success:
P(I get out of bed on third snooze) = (1-P(I get out of bed on first snooze))*(1-P(I get out of bed on second snooze))*P(I get out of bed on third snooze) = (1-2/5)(1-2/5)(2/5) = 18/125 ~ 20/120 = 1/6 ~slightly below 0.2, I’d say around 0.18 = => 18%
Then I went to sleep again and got out of bed on the 4th snooze alarm.
btw: The probability of me ever getting out of bed on my snooze alarm, found by summing over all probabilities from 1 alarm going off to infinitely many snooze alarm events, is 1, as you’d expect. So it was bound to happen, eventually…