Introduction to Computer Programming with MATLAB
CEE/MAE M20
Lecture 4b
and Random Numbers
CEE/MAE M20
2
Watch:
http://youtu.be/E7DKxe_m1AM
http://youtu.be/vuMir11YFPs
CEE/MAE M20
3
•
Also known as Galton Board or Quincunx
•
A device for statistical experiments
•
Invented for demonstrating how the
normal
distribution
approximates the
binomial
distribution
for a large number of events.
Figure
 Results of three different Galton Board experiments. Notice
that all boards have the same number of rows (thus identical board
arrangements), but the number of dropped balls in each case is
different.
Bean Machine
CEE/MAE M20
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Figure
 A variant of Galton Board in which
only the nails that can potentially be hit by a
ball dropped from the funnel are included,
leading to a triangular array instead of a
rectangular one.
Bean Machine
•
Upright board with evenly spaced nails (or pegs)
•
Nails are arranged in a
staggered configuration
•
Balls collected in heaps in evenlyspaced bins at bottom
•
Each time a ball hits one of the nails, it can bounce right
(or left) with equal probability.
•
If the number of balls is sufficiently large:
The distribution of the heights of the ball heaps will
approximate a normal distribution.
CEE/MAE M20
Objective
5
Some assumptions
1.
No dropped ball goes outside of the board.
2.
Subsequent to hitting a peg in one row, a ball can only interact with the peg
immediately to the left or the right of that peg in the row below it
3.
A ball cannot fall through a row without interacting with a peg
4.
Balls fall directly into the bins after falling past the last row of pegs.
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 Summer '06
 ArunPrakash
 Computer Science, Computer Programming, Randomness, CEE/MAE M20

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