Lack of Memory Property

"For x, y > 0,

P [ X > x + y | X > x] = P [ X > y]

We can interpret this as follows.  Suppose that X represents the time, measured from now, in weeks until the next insurance claim is filed by a company, and suppose also that X has an exponential distribution with mean 1/t.  Suppose that 5 weeks have passed without an insurance claim, and we want to know the distribution of the time until the next insurance claim as measured from our new time origin, which is 5 weeks after the previous time origin.  According to the lack of memory property, the fact that there have been no claims in the past 5 weeks is irrelevant, and measuring time starting from our new time origin, the time until the next claim is exponential with the same mean 1/t.  In fact, no matter how many claims have occured in the past 5 weeks, as measured from now, the time until the next claim has an exponential distribution with mean 1/t; the distribution has "forgotten" what has happened prior to now and the "clock" measuring time until the next claim is restarted now."

Peace out.

Eating It

I ride my bike to and from classes to save time; I'm sure like everyone who reads this knows that.

Last Friday, after my Stat 415 class, I hopped on my bike in the bike "parking lot" that's right outside of Willard, on its east wall.  Typically I just stand beside my bike and walk it north a little bit until I'm on the main road until there are less people, but for some reason I decided to just hop on right away that day and hope for the best.

So I hop on, and start going toward the busy sidewalk.  There were a lot of people.  I remember there was a girl coming from my left, I think she was Asian, and some guys coming from the right.  I didn't want to thread right between them, so I tried to stop.  I put on the brakes, and I turned my wheel a sharp left, as if I might go behind the girl coming from my left somehow. 

I guess I turned my wheel too far, and I pedalled a tiny bit and then IMMEDIATELY just hit the deck.  And I totally ate concrete in front of everyone.  I'm sure there were hundreds of people in the area, but I don't know how many were watching.  I didn't know what to do, I felt really embarassed, so to try to dispel some of the awkwardness I used my loud Will Ferrel voice and said, "WOW THAT WAS RELLY EMBARASSING."  I got back up and just started walking, and realized the knee of my pants were all wet and sort of dirty.

The kid named Mark in the room next to me was walking by without my noticing, but then he said, "Good going," or something to that effect.  I told him I was going to walk with him because I'd feel less like a loser, and as we were walking he said, "So, uh... you might want to learn how to ride a bike a little better."  I agreed.  We got to the road at the north and I rode to my next class, where no one knew what happened.

Peace out.