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Unformatted text preview: AMS 311 (Fall, 2009) Joe Mitchell PROBABILITY THEORY Homework Set # 7 Due at the beginning of class on Tuesday, November 24, 2007. 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 . 5 integraltext 1- x x x 2 e y dydx in this form. Read: Ross, Chapter 6, Sections 6.4, 6.5; Chapter 7, Section 7.5 and Section 7.7; and handout on expectation. SPECIFICS OF READING ASSIGNMENT: Examples to read carefully: Chapter 6: 4a, 4b, 5a, 5b Chapter 7: 5a, 5b, 5c, 5d, 5k, 5l, 7a, 7b, 7d, 7e, 7f, 7g, 7h (1). (15 points) If E (3 X ) = 1 and var (2 X ) = 5, find (a). E [(2 + X ) 2 ] and (b). var (4 + 3 X ). (2). (15 points) The random variables X and Y have a joint density function given by f ( x, y ) = braceleftbigg 2 e- 2 x /x if 0 ≤ x < ∞ , 0 ≤ y ≤ x otherwise Compute cov ( X, Y ). (3). (30 points) [See examples 5a, 5b of Ross, Chapter 6.] Let X and Y be continuous random variables...
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This note was uploaded on 02/07/2010 for the course AMS 311 taught by Professor Tucker,a during the Fall '08 term at SUNY Stony Brook.
- Fall '08