hw8 - AMS 311(Fall 2009 Joe Mitchell PROBABILITY THEORY...

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AMS 311 (Fall, 2009) Joe Mitchell PROBABILITY THEORY Homework Set # 8 Due at the beginning of class on Thursday, December 3, 2009. Reminder: Show your reasoning! You do not need to evaluate arithmetic expressions or integrals, if they are fully specified. For example, you may leave integraltext 0 . 5 0 integraltext 1 - x x x 2 e y dydx in this form. Read: Ross, Chapter 6, Sections 6.4, 6.5; Chapter 7, Sections 7.2, 7.4, 7.5 and Section 7.7; and handouts on expectation and rat-in-maze problems. SPECIFICS OF READING ASSIGNMENT: Examples to read carefully: Chapter 6: 4a, 4b, 5a, 5b Chapter 7: 2a, 2c, 2e-h,, 2i-j, 5a, 5b, 5c, 5d, 5k, 5l, 7a, 7b, 7d, 7e, 7f, 7g, 7h. (1). (16 points) Consider the maze shown below. There are three cells (Cell 1, Cell 2, and Cell 3) and two deadly (quite permanent) outcomes (Death By Poison, and the dreaded Death By Torture). A rat is initially placed in cell 3. When the rat enters Cell i , he wanders around within the cell for X i minutes, where X i has density f ( x ) = braceleftbigg 2 x if 0 x 1 0 otherwise,
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