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

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

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### 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
Ask a homework question - tutors are online