MS_E220+Exercises+Booklet

MS_E220+Exercises+Booklet - CHIU, Probabilistic Analysis:...

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Unformatted text preview: CHIU, Probabilistic Analysis: Structuring, Processing and Communicating Probabilistic Information 1 Exercises Probabilistic Analysis: Structuring, Processing and Communicating Probabilistic Information Exercises Copyright September 2010 Samuel S. Chiu Stanford University Stanford, CA 94305-4023 USA samchiu@stanford.edu (Do not circulate or duplicate without permission from the author) CHIU, Probabilistic Analysis: Structuring, Processing and Communicating Probabilistic Information 2 Exercises Background Math and What you need to know about spreadsheets You will be asked to use spreadsheets for some of the assignments (homework and take-home). We do not expect you to be an expert in spreadsheet programming (e.g., writing a macro program). However, you should be able to do the following operations: Using spreadsheets as a calculator to perform parametric and sensitivity calculations: identifying/defining input cells (for easy parameter changes), defining cell names (so that your spreadsheet program can be read and easily understood by you one day later). Simple cut, copy and paste functions. Simple drag to copy functions. Using spreadsheets to implement difference equation iterations: one and two dimensions. Using simple spreadsheet graphic utilities. Using spreadsheet special library functions (e.g., statistical which we will use in Chapter 13). See also Appendices B and C of the text. The following spreadsheet exercises represent the level of expertise expected of you. There are also a few simple algebra and calculus exercises. 1. Define/name an input cell as Total . You can then assign a value to Total by changing the value of that cell. For example, entering a value of 10 in that cell, Total will take on the value 10. Now define the following difference equation: a. Compute P ( n ) on a spreadsheet. You should be able to change the value of Total and observe the impact on P ( n ). b. What happens when n exceeds Total ? Generally, you have to be careful and understand the range of of the indices over which the difference equation is valid and to account for possible boundary conditions. c. Plot P ( n ) as a function of n . d. This system of difference equations represents a solution to the birthday matching problem, p. 3.6 of text (double, not triple). When n = 23, P ( n ) ~ 0.5 2. Implement the Pascal triangle on a spreadsheet (p. 2.7 of text) This is a two-dimensional system of difference equations one way to numerically compute the Binomial coefficients, . Why do we want to use a system of difference equations to compute the Binomial coefficients when we know the exact formula? Using CHIU, Probabilistic Analysis: Structuring, Processing and Communicating Probabilistic Information 3 Exercises the formula gives you one numerical value for a specific pair of ( n, k ). If you want to compute , you have to carry out the multiplication, factorial and division from scratch. The work expanded to calculate...
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This note was uploaded on 09/28/2010 for the course MS&E 220 taught by Professor Chiu during the Fall '10 term at Stanford.

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MS_E220+Exercises+Booklet - CHIU, Probabilistic Analysis:...

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