fall09final - University of Illinois Fall 2009 ECE 313:...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
University of Illinois Fall 2009 ECE 313: Final Exam Tuesday, December 15, 2009, 8:00 a.m. — 11:00 a.m. 100 Materials Science and Engineering Building 1. [60 points] (3 points per answer) Mark TRUE or FALSE for each statement below. No justification is required, but to discourage guessing, 3 points will be deducted for each incorrect answer (no penalty or gain for blank answers). A net negative score will reduce your total exam score. (a) A , B , and C are events such that 0 < P ( A ) < 1, 0 < P ( B ) < 1, and 0 < P ( C ) < 1. TRUE FALSE ± ± P ( A B ) = P ( A c B c ) - P ( A c ) - P ( B c ) + 1 . ± ± P ( AB ) P ( A ) + P ( B ) - 1 . ± ± P ( A c | B ) P ( B ) + P ( A c | B c ) P ( B c ) = P ( A c ) . ± ± P ( A c | B ) P ( B ) + P ( A | B ) P ( B ) = P ( B ) . ± ± P ( A c | B ) P ( B ) + P ( A | B c ) P ( B c ) = P ( A B ) - P ( AB ) . ± ± P ( B | A ) = P ( A | B ) P ( A ) /P ( B ). ± ± If A and B are mutually exclusive events, then they are independent events. ± ± If A , B , and C are independent events, then P ( ABC ) = P ( A ) P ( B ) P ( C ). ± ± If P ( ABC ) = P ( A ) P ( B ) P ( C ), then A , B , and C are independent events. (b) X is a continuous random variable whose probability density function f X ( u ) is an even function , that is, f X ( u ) = f X ( - u ) for all real numbers u . Let F X ( u ) denote the cumulative probability distribution function (CDF) of X , and assume that that var ( X ) = 4. TRUE FALSE ± ± F X ( u ) = F X ( - u ) for all u, -∞ < u < . ± ± E [ X 2 ] = 4. ± ± E [ | X | ] = 2. ± ± P { X > u } = F X ( - u ) for all u, - ∞ < u < . ± ± P
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/15/2010 for the course ECE 313 taught by Professor Sarwate during the Spring '08 term at University of Illinois at Urbana–Champaign.

Page1 / 3

fall09final - University of Illinois Fall 2009 ECE 313:...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online