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Probability and Random Processes - Problem | EECS 501, Study notes of Electrical and Electronics Engineering

University of Michigan (UM) - Ann ArborElectrical and Electronics Engineering

Material Type: Notes; Class: Prb&Rand Proc; Subject: Electrical Engineering And Computer Science; University: University of Michigan - Ann Arbor; Term: Unknown 1989;

Typology: Study notes

Pre 2010

Uploaded on 09/02/2009

koofers-user-fcb
koofers-user-fcb 🇺🇸

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T eM PRopLEM: sIVEN X,Y ABE 2 VECTEE JOINTLY GAUSSIAN BOND TABLES, pe nell = Prove Suse (Y= Efsly=Y] =[ECx) + Kxy ky CY ~€Cy2) WHERE Kxy = E[ (8-€(8))(y-E(y)) ] AND ky=kyy. t e7 (E-Elx1y])"kyy! (x-Elxty) /2 PROOF: we SHOW Pay SID) = Saye | “s = ky —Kayky Kny WHERE E(xty)= E(x) + Rryky (Y-ELY}) AMO Kyiy = Rx ~ Rayky Sey THE PEsiIRED RESULT Fetcows IMMEDIATELY. NeTE €ee*) (MOEPENOEMT =_ 4 SINCE FomTLy GAUSSIAN. — 2 - (*-fea le ky ie. Tv - i, . = (20)"* Ig "2 © (E ~ an spl). (s-(e Ibo crepe SINCE Ry’ = Kxty (Defined Aowe) weAREoowe. ST ES MoTE THAT Rv) SECEI+ key ky (YE(Y)) I CETT LINEAR LEAST-SOVARES ESTIMATE oF yx ciVeW Y= . THIS CAM DE DERIVED AS WN SCALAR CASE ArtHOUGH MESSIER