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ps1 - N i denote the number of times the dart lands within...

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EE 497B PROBLEM SET 1 DUE: 5 Feb 2008 Reading assignment: Ch 1. Problem 1: Yates Problem 1.2.1 (10 points) Problem 2: Yates Problem 1.2.2 (10 points) Problem 3: Yates Problem 1.4.1 (10 points) Problem 4: Yates Problem 1.4.4 (15 points) Problem 5: Yates Problem 1.4.7 (20 points) Problem 6: Yates Problem 1.5.1 (10 points) Problem 7: Yates Problem 1.5.2 (10 points) Problem 8: (15 points) In this problem you will use a series of identical experiments, simulated in MATLAB, to estimate the value of π . A dart board with diameter of 1/2 is centered within a square-board with sides of unity length. A series of N identical experiments are performed. The procedure consists of throwing a dart at the square-board, and the observation is determining if the dart falls on or off the dart board. The experiment model requires that the dart always lands within the square-board, and that the dart is equally likely to hit any specific point within the square-board. Let
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Unformatted text preview: N i denote the number of times the dart lands within the dart board for N experiments. 1. (8 points) Estimate π as a function of N and N i , and denote your estimate as θ . 2. (7 points) The MATLAB command x = rand( [N,1]) generates a column vector of N numbers, where each number lies in the interval [0 , 1], and each value in this range is equally likely to occur. Using this function, ±nd and plot θ as a function of N for 2 ≤ N ≤ 10 6 . In order to receive credit, include your name and section at the top of the m-±le, appropriately label the plot axes, provide a suitable title for the plot, and add your name and section number to the ±gure using the MATLAB command gtext ....
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