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hw9_sol - Problem 2 fisté—mwmtl—m...

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Unformatted text preview: Problem 2 - ( ) fisté—mwmtl—m ( ) E—(fl—zwfimtl-é} h 3,}; ‘2 —-———-————“ 9' 3,3! = ———'—'—"'—" 21rfi1—p? 2e'1/1—pg 1 1 3-?” awe) =§f_:h(x.y)dy+— mama: «,5 Similarly E—flz fl’(y)— J2? .'. X and Y, individually, are Gaussian RV‘s. b) However, 1 _ Fae—[B-RHWFI’EU-‘Fgl + 1 _ ng-{32"2HWH2(1_#§) firm?) = ' 2r\/l——p2\/l——p’ does not have the form required for jeiutlz Gaussian RV’s. K51 Q Y2 4’ .JL'R. J *3 _ :3... j 2* (Ed “/51 "7.2 Pitxxwi; ’iétfl - Pfxévq] PFVaaj .E W a x C“ 1 4i aim} @W‘E’fl. [I 3: Art-*1 :1 ‘1 firm a 2 *“ fi-ma g .. "” W >214 72") "‘ ‘11“:in 37mewflf) 4 73) w WK<Vg> flvm’z) Problem 4 E *{31 +3211” 4 a Hwfikfigfl ffflfiw—jgwhfi ff f; ifidrda let z=rcosfl, y =rsinl? =]_-- e 2 Note: 1M)?” + Y2 has a. Rayleigh dist- 7:} ‘3“ = 21.112 _r2’:2 = l b) Phr‘X” + Y1 :2- r] = 6’31” from above. For (any) such that 1:2 + 92 2: r3 fxy£$1 y|R ‘9 r)dmdy PI: <X£m+dm,y r: Y Ey-I-dyIR} r] fxy(m,y)dzdy FIR 3." T] fxflflw) - Pmbfl 1549+»? —r=m 2w ‘1'? fXY(r1yiR :3" I") II [I Problem 5 Problem 6 6. a) mix) = fifty—£9263: b) Km) = f(ylm)f(m) f($t y) = 2:0'N EXP (— c) 111:) (first: + (y - 3:)2 ll 'i“-~ g S 11*: “bl- 55 & II ’5‘ 2n + H 1“Ind-I" l—‘—I H H | h: u t: || F5. Q 2M + 1...: ‘I-u-I" l'—-""_—‘l .--""""'-.. H | it: || Pa. 2"» + H V H | H + w [—- II ‘--.... B H. H “H 1:: ‘n—n’ & fly) il |—| 1: I “v: H || pal. 11} x 'U 'l H E II |—|. A M q «mag; + 1) exp " flipflfflyl f(:rly) (st-~10) 1 20'}; II fl 2% + H V H H I M I: H .l. “:2 N 1 (m-fly)’ = 52 exp 1T 21:5; 2W+1+d N Problem 7 CL» 9‘? _WI1Z “ MF'S 1 Tm f' (u i A? ‘2‘ G 1‘?- _W_1__ 362% Ll 0 . _ C2) I i x‘meLKQ” :3qu,511») It” d "32 11 E ( t 0 \Csrlwz) *2 Ehsjgw/Lufl L "2372 ET C wt?) 00 MO IIIIIIII ' 4‘» “‘3 $3 I $7 N R $ "‘2 2 Z 72> W“ ‘ 232 p h W11”; 3: 2*“ WU 1m ~ :2 2» Hg 4 I r I AK XCq/fiq) ”7.2.5. ----------- ...
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