# Second movement sketch

I’ve been beating my creative head against the wall awhile, and finally, today, I came up with something. The melody is beautiful in its simplicity. The star player most of the time is the piccolo, which should make it happy, since it only got to play about three lines of music in the first movement. Anyway, this is just a sketch: I’ll probably keep the melody and the impressionistic piano stuff, but how those end up realizing themselves in anybody’s guess (Oh, and by no means do I consider the end of this recording an ending; it was just where I decided to stop today). This is a turning point in the dynamical system of composition, so feedback will have the most effect now. If you have any ideas, please speak up before I get too attached to what I’ve done. MIDI|MP3

## 4 thoughts on “Second movement sketch”

1. Trieu says:

Luke, “delete” or “not delete” is not an important issue. However, I would expect you to come
to
http://en.wikipedia.org/wiki/Free_ticket_problem
to tell me whether those my events are “independent”! many people they say “NOT”.
Thank so much!
Trieu.

2. What an interesting place to have a discussion about probability, in an entry called “Second movement sketch”. Consider it a cookie for the math nerds who decide to listen to my music.

In the “sequential” approach to the problem that you’ve taken, the events are not independent. Consider three students. The probability of the first getting the ticket P(1) is 1/3. The probability of the second is P(2) = P(1′)P(2|1′) = (1-1/3)(1/2) = 1/3. And the last student is: P(3) = P(1′)P(2′|1′)P(3|2′,1′) = (1-1/3)(1-1/2)(1) = 1/3. That’s awfully complicated though. You could make the ticket a uniform random variable in the envelopes (which you’ve done anyway) and ask which envelope it’s in. And then it’s just 1/3 for each.

3. Trieu says:

Thank for that, Luke
I do aware my solution was wrong since the sum of probabilities does not equal to 1. Anyway,
your conditional probability solutions above is a pretty and precise expression of “each student does have
equally chances”.