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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 Widjija’s 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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This note was uploaded on 03/18/2012 for the course ECE 861 taught by Professor Shroff during the Spring '11 term at Ohio State.
 Spring '11
 shroff

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