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Unformatted text preview: CSEECE 861: Homework 1 Due in class by: Wed. Feb. 1, 2012 (1) (4) Solve problems 1.2, 1.5, 1.9, 1.15 from Leon Garcia and Widjijas book (Second Edition). Probability Review Problems (5) (11) (5) Prove that finite additivity follows from countable additivity (6) From the axioms of probability, prove the following: For an event A and its complement A c , prove that P ( A c ) = 1 P ( A ) If A B , then P ( A ) P ( B ). (7) Let X be a nonnegative random variable with distribution F . Show that E ( X ) = Z P ( { X > x } ) dx. and E ( X n ) = Z nx n 1 P ( { X > x } ) dx. (8) X and Y are random variables. (a) Show that E ( X ) = E ( E ( X  Y )). (b) If P ( { X x,Y y } ) = P ( { X x } ) P ( { Y y } ) then show that E ( XY ) = E ( X ) E ( Y ), i.e. if two random variables are independent, then show that they are uncorrelated. Is the reverse true? Prove or disprove....
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 Spring '11
 shroff

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