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Unformatted text preview: Y which is a whitened version of X . Problems from Grimmet & Stirzaker 1. Ex 3.7.5. What is requested is E [ T-t | T > t ], i.e., the mean subsequent lifetime given that the machine is still running after t days. Then use the hint from the book. Note that in (a), P ( T > t ) = 1 N +1 ( N-t ). 2. Ex 3.7.7. Hint: Show that P (robot faulty | fault not detected) = (1- ) 1- 4 = . Hence argue that the number of faulty passed robots, given Y , is distributed as B ( n-Y, ), which has mean ( n-Y ) . Hence show that E [ X | Y ] = Y + ( n-Y ) . 3. Ex 4.1.1(a) 4. Ex 4.1.2 5. Ex 4.2.1. Hint: think geometric r.v. 6. Ex 4.2.2. Hint: P (max( X, Y ) v ) = P ( X v, Y v ). 7. Ex 4.4.1. Hint: integrate by parts. 8. Ex 4.6.4(b) 2...
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This note was uploaded on 03/01/2012 for the course ECE 6010 taught by Professor Stites,m during the Spring '08 term at Utah State University.
- Spring '08