So we’re covering randomness today.  And Wikipedia (yeah, not very original, I admit, but it works) defines randomness as “lack of pattern or predictability in events”.  And how do we know how random or how predictable something is?  Well, one way is to look at the distribution of the data and the probabilities associated with it.  So let’s say tomorrow as I’m getting ready for work and I can either put on my blue suit, my dark pink suit, or my peach-colored suit that OMG looks exactly like the St. John at Neiman Marcus (never mind I got it at JC Penny for a tenth of the price).  Although I’m partial to the last one, let’s put an equal probability of me picking either one to wear to work the next morning.  In that case, my probabilities follow a flat distribution like the uniform distribution and we could say that such a scenario would be an almost completely if not completely random case since you probably couldn’t predict what I’m going to wear.  Okay, I’m lying and you know I’m going for the peach-colored one but again, lets assume equal probabilities for the sake of our example.  Now, say you wanted to predict what time I get to work and you knew I usually get in around 8, give or take 15 minutes.  You would put higher probabilities on times between 7:45 and 8:15 in that case and lower probabilities on times earlier or later than that interval.  And your distribution of probabilities might look symmetric like a normal distribution.  So in that scenario, you would probably be right if you predicted that I indeed arrive at the office between 7:45 and 8:15.  So, while there is randomness involved, it’s much less than in my wardrobe scenario, my partiality to the peach-colored suit notwithstanding.

Now, for something completely different, lets say I’m not going into the office tomorrow because … wait for it … George Lucas is flying me into Los Angeles where we will be discussing a possible Order of the Dimensions movie deal.  Now, the distribution of probabilities associated with that is most likely very skewed, like a gamma distribution would be, where the probability of that not happening is much, much higher than of it happening.  So if you predicted that it’s not gonna happen, you were probably, most likely, unfortunately right.  So we could say that this scenario would constitute a least random case of all the cases I predicted.  So there you have it.  Just a bit about randomness and how it can be related to the distribution of probabilities.  Join me next time as I continue this discussion, talking about random walk, after which we may introduce the Metropolis-Hastings algorithm and how it has nothing to do with the Metropolis movie.  Okay, maybe it does.  We’ll see.  Now what to wear to work next?  Hmmm …

See?  Just like the St. John at Neiman Marcus!  Well, okay, it would more likely look like this if I looked like that model — but you get the picture.