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Unformatted text preview: EE5620 Stochastic Processes 1 EE5620 - Homework #1 Solutions 1. This problem is not graded. For interested students, you can go to http://my.opera.com/zachminami/blog/index.dml/tag/Paradox or http://www.math.toronto.edu/mathnet/games/montymath.html for a correct answer. 2. This problem is not graded too. Let R denote the event that the radar registers the presence of an aircraft and N denote the event of no aircraft presence, respectively. Then the probability of false alarm is P [ N ∩ R ] = P [ R | N ] P [ N ] = 0 . 1 × . 95 = 0 . 095 . The probability of missed detection is P [ N c ∩ R c ] = P [ R c | N c ] P [ N c ] = 0 . 01 × . 05 = 0 . 0005 , where the superscript c means complement. 3. The conditional variance of X given Y = y is defined by Var( X | Y = y ) , E £ ( X- E [ X | Y = y ]) 2 | Y = y / . Carrying out the above gives Var( X | Y ) = E [ X 2 | Y ]- ( E [ X | Y ]) 2 ....
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