Recitation 6 Solutions

Recitation 6 Solutions - Steven Weber Dept. of ECE Drexel...

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Unformatted text preview: Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2010) Recitation 6 (Friday, May 7) Question 1. Consider a presidential election between two candidates (A and B) in a country of n voting citizens. The citizens agree to elect a candidate at random in the following way. Each citizen votes for candidate A with probability p or for candidate B with probability 1- p . Let N A ,N B be the number of votes received by candidate A,B respectively. Note that N B = n- N A . Note the event that the absolute value of the deviation of a random variable X around a center point c being less than d , i.e., {| X- c | d } , equals the event { c- d X c + d } . 1. Give an expression for the probability that the difference in the number of votes received by A and B is less than d ( n ). Simplify your answer as much as possible. P ( | N A- N B | < d ) = P ( | N A- ( n- N A ) | < d ) = P ( | 2 N A- n | < d ) = P ( n- d < 2 N A < n + d ) .....
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