This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: EE 562a Homework Set 3 Due Wednesday 14 Feb 2007 1 (The following welldefined problems come from different sources, and the notation used may vary. Don’t let that bother you!) 1. Let y ( u ) be a real random vector with mean vector m y and covariance matrix K y given by m y = 10 10 K y = 2 1 1 2 . (a) Sketch the regions of the yplane to which each of the following events pertain, and numerically upper bound the probabilities of these events. A = { u ∈ U : y ( u, 1) < } B = { u ∈ U : [ y ( u, 1) y ( u, 2)] / 2 > 20 } C = { u ∈ U :  y ( u ) m y  > 10 } (b) Given the additional information that y ( u ) is a Gaussian random vector, determine precise values of the probabilities of the events A and B above. (You may need a table of tail integrals of the onedimensional Gaussian density to do this, e.g., Table 26.1 in M. Abramowitz and I. Stegun, Handbook of Mathematical Functions . If the table does not go far enough to suit your purpose, any of the asymptotic expansions 26.2.1226.2.15 may give you an accurate answer with a small amount of work.) (c) Given the additional information that y ( u ) is a Gaussian random vector, determine upper and lower bounds to the probability of the event C above. There are several ways to develop such bounds. For example, you could inscribe and circumscribe appropriate ellipses around the region of integration C and apply the results of problem 1. Or youand apply the results of problem 1....
View
Full Document
 Spring '07
 ToddBrun
 Probability theory, random vector

Click to edit the document details