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Review-quiz2 - lJ rs.re"te poir U?r L-onT\vlzLtou,Jr{| g M...

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lJ rs.re"te ,Jr,{| gMf ' f t,v*'! 4o 7ap^, (r,y) = ) ^ ), '/ " Mamivq{ 0uFsr *ff 'P{s} " .f&flxvrny) 6<'1kt} fl*r (x,3) = kfi= qftv{x3} 1' Prftl) " q-fuv{r,g ry' $(*'Y): f,w (u, ) = Lf- F*,-, {x,rl (x,3'l;grx,1t,,* u o ),Y ./^\ fx Pn,, (xr3): p[x"" il ELxtvl= f"fl*', X indn{ w}'n,rvt @ Y k, j)' fx{x) fv d1) til"ry&.)S E[w},46nr*,5t frrtr,y) f\ r\ . fi ^ -a o t,ond-,lt1qy\oX flM l- ; txy) poir: *,{ U* ,?r L-onT\vlzLtou: - EI!_!LF , F* ,, (x,l , p -(r<r, y*S pfr=", y = j) " _*L_Iur &v rrji " TfuTJuu ,c-i|-. J -ffi]X{.* " {xryfx ,\) >, i'f{,1,,,,))or ,Prc) ={ftxyrx,jrd*fu tp flfi,tsi^) F"Q M o rginil PDFs , (x q) ry ,xd I' tx ) Y( ll + :l ,-_f{r,v(r, }* '^f{^n{x,g} Qe - IEn*n ivr xv gfiaw Lbr rcepar.c fr ave*att {S. XrV inC*(L,AAand. e {; c,.,?) "{*at d,\} # N'1 f x,v) q;rr,o= i( e^,, (x3r dry :J lO{r,g){x,y(x,y}d . Gndit\onC pdf : {*,n(*,J) = fu-$- er fv {Yi =Lx lY I : Lnf,n, ('gctx E[l'llJ,
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n F /\ , tl I r l-nirs _j\ t{[email protected]_" Vqrj_$fu}s " Ex(e*?\o_n^, - Fo *- erv\A nqy\d.ona va ric& lsJ X o*t{ Y, U a [x* Y] = L[y]" EIY ] Ccfr"e -A^,ttovr coefl6iqi€#rf , f^,* - X,Y utA1nwe-Ls'twl <e kvfr,ti= o X rY on thSo vrcu( @ E tX,y J= o ' Fun, c+ ions a$ two RVs, [ *nn't-tvreao,nq Voc [x* Y] = V*rflyl * W*qr f,vl + ] Lf (r/,ltv Ttnv]] Cov.rr iqn ca ', OoV [x tyJ = g[ t x*/*)ty lr)J Co nrolal ion, fr,v = g[xVJ = Cavtx,yJ \ ^ i nd,nye*ilLrt qn,o,,r" Case ) W53{r,v) , &"J, W"rvrax(r'y)) w=X*Y, px[= Y, g\f: rnin(x'y) F, (*) = P(W sN) * p [rn\6fnv) { *}: J- ff*ivrtvuY} tsu} = ' 1- "P( x>br, vl*:) = f - Jf*" rY(Y\J)d "4 4* S te-p {lr.ot. Fw (r^,) : p {W * u,) - J*o\ Jt"f 1-o t o t"t" de$ivasiua* to 3at ( m H: Wrv)^Ax[x,v) r Fw [ur)" p[\{ srd)" ([rrux(x,v)su) = P(X<H) y<r*) =
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