final

# final - Homework 10 Section 7.1 problems 2 5 Section 7.2...

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Homework 10 Section 7.1, problems 2, 5, Section 7.2, problems 2, Section 7.3, problems 8. Exercise Problems for Final Exam 1. Suppose that random variables X and Y have joint density function of the form f ( x,y ) = Ce -| x + y |-| x - y | . Determine the value of C , ﬁnd the marginal density function of X and Y , ﬁnd E ( X k ) ,V ar ( X ), ﬁnd E ( XY ) and σ XY = E ( XY ) - E ( X ) E ( Y ), ﬁnd the conditional density function f Y | X ( y | x ), ﬁnd the conditional expected value E ( Y | X ), 2. Let X and Y be independent uniformly distributed random variables taking values in the interval [0 , 2]. Find the density functions of Z = X + Y and W = X - Y . Are Z and W independent? What is the covariance σ ZW = E ( ZW ) - E ( Z ) E ( W )? Are they uncorrelated? 3. Let X 1 , ··· ,X n , ··· be an i.i.d. sequence of random variables having 1 - e - λx : x 0 and 0 : x < 0 as their common distribution function. What is the distribution function of

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## This note was uploaded on 09/04/2010 for the course EE 464 taught by Professor Caire during the Fall '06 term at USC.

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final - Homework 10 Section 7.1 problems 2 5 Section 7.2...

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