Mar 3
quiz 1
... during about the first half of class.
aside
probability games
One more assignment before the break :
- in groups of 2 people, invent a dice/points/pig-like game
- come to class a week from today (Thu before break) to explain how it works and what the probabilities are
- ... and do a writeup on any of the invented games, due soon after.
We can use R to simulate these sorts of games, and from those numerical experiments see what's going on.
Here's Matt's R code to simulate pig
And here's mine:
Doing this in R is essentially a programming task which is, I expect, outside the scope
of what this course will cover. But you may be able to adopt Matt's script for your game.
starting chapter 3 - the bell curve
If there's time, start talking about the "normal" or "bell" or "gaussian" probability distribution.
One way to get at it: flipping a coin and counting the number of heads.
Discuss this pattern (Pascal's triangle)
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
... and what it has to do with this situation.
What will the hundreth line look like?
# R code
# The choose(n, m) function gives the m'th element
# of the n'th row of Pascal's triangle, which is
# also the number of ways to choose m things from a pile of n of them.
> x = 0:100 # 0, 1, 2, 3, 4, ...., 100
> y = choose(100, x) # 100'th row of Pascal's triangle
> plot(x, y) # the binomial distribution - approximately normal
> plot(x[25:75], y[25:75]) # just the middle part
The normal curve is a universal, special distribution which shows up all over :
any probability distribution (even the coin flip [0.5, 0.5])
will turn into a normal distribution if it is added together many times.
