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Unformatted text preview: Mathematics Department, UCLA P. Caputo Fall 08, midterm 2 Nov 19, 2008 Midterm 2: Math 170A Probability, Sec. 2 Last name First and Middle Names Signature UCLA ID number (if you are an extension student, say so) Please note: 1. Provide the information asked above and write your name on the top of each page. 2. The only thing you may use during the exam is a pen to write down your answers. Every- thing else (calculator, textbook, notes, your own paper, . .. ) has to be put away safely. 3. Cheating in any way will not be tolerated. Do not speak during the exam. 4. Show your work and explain what you are doing. This is more important than just finding the right answer. 5. You can use the blank pages as scratch paper or if you need more space to finish the solution to a question. When you continue on another page indicate this clearly. 6. The maximal number of points attainable is given at the beginning of each question. Good Luck! Question 1 2 3 4 5 Total Score out of 10 10 10 10 10 50 Name: 1. (10 pts) Consider independent rolls of a fair die. Let X denote the number of rolls needed to see the first even face and let Y denote the number of rolls needed to see the first face larger than 3. Find: a). E [ X ] and E [ Y ]. b). P ( X > 2 | Y = 2). c). P ( X = Y ) Solution . a) X and Y are both geometric random variables with parameter p = 1 2 . Therefore E [ X ] = E [ Y ] = 1 p = 2 ....
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This note was uploaded on 11/01/2009 for the course MATH 170a taught by Professor Staff during the Fall '08 term at UCLA.
- Fall '08