Unformatted text preview: AMS 311 (Fall, 2010) Joe Mitchell PROBABILITY THEORY Homework Set # 7 Due at the beginning of class on Tuesday, November 23, 2010. 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 “Notes on Expectation, Moment Generating Functions, Variance, Covariance” 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) (a). If E (3 X ) = var ( X/ 2) and var (2 X ) = 3, find (i). E [(2 + X ) 2 ] and (ii). var (4 + 3 X ). (b). Suppose that X and W are independent and that var ( W ) = 7, E (( X- W )( X + W )) = 100, E (3 W ) = 30, E ( X 3 ) = 60, and E ( X + W ) = 12. Compute (i) var ( X ) and (ii) cov ( X 3 ,W 2 ).....
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