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lecture4b - Introduction to Computer Programming with...

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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 4 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 evenly-spaced 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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