THE ROYAL STATISTICAL SOCIETY 2016 EXAMINATIONS SOLUTIONS GRADUATE DIPLOMA MODULE 1

Transcription

1 TH ROAL TATITICAL OCIT 6 AINATION OLTION GRADAT DILOA ODL T oci i providig olio o ai cadida prparig or aiaio i 7. T olio ar idd a larig aid ad old o b a "odl awr". r o olio old alwa b awar a i a ca r ar valid alraiv od. Alo, i a ca wr dicio i calld or, r a b or valid poi a cold b ad. Wil vr car a b a wi prparaio o olio, oci will o b rpoibl or a rror or oiio. T oci will o r io a corrpodc i rpc o olio.

2 Qio i ii [diribio ig b iplici] p o = + + =.½ + [ ar] = ½ + [ ar] = = 6. = Var a T rag pac o i {, 3, }. or a i i rag, c] [idpd. ad b ppo a =, or o grar a or qal o. T a val i rag,,,. or a i i rag, ad o, codiioal o =, a diribio o i wi =. =, Var,,,,,

3 3 Qio i ii = d d d!! ] [wr!!! iilarl,. [Giv ar alo i ll worig ow.] o,. Var a >, d d ig par i, wi = ad θ =, =, Var = ½. b, d d d d!! ] [ c ig Law o Irad pcaio, } {,,,,

4 Qio 3 i ii iii p ] [ p α d d θ o p p a coa or i =, b dcra wi i < < [Do d o a > o g cod o ar.] G = ir copo ail i i = or = + ad = +. [idpdc] = +. [Giv ll ar o cadida wo rali rvivor cio o b prodc o rvivor cio o ad.] g = G = +.. G g I Wibll ca, Ti i aard cio o aor Wibll diribio. G = C ad C ail i i =. [idpdc] W wo copo ar idical, G = [] ad g =.. o.. ic bca.,,,

5 Qio a i Cov, = [Var.Var] = 6 ad Cov o 5 5 T ii T rado vcor a a bivaria oral diribio, wi, , b Cov [Cadida wo.5 iad o. i calclaio old b awardd ll ar.] iii T corrlaio bw ad i -.5, a a corrlaio bw ad. Ti illra gral poi a r-calig rado variabl or apl, b cagig i o ar cag ir covariac b o ir corrlaio. i = 3 =, 3 = ii i orall diribd wi 3,, Var / 3 / / 3 / 3 / 3 / 3 iii a a livaria oral diribio wi μ μ α, Cov μ α σ σ ρ σ ρ σ σ σ ρ ρ σ ρ σ ρ σ, 5

6 Qio 5 i ii iii I i ca, = ad =. ig = 3, i = ad j = 3 giv g 3!!!! w, v w. v w. v. 6w, w v W V 6 w 6 w 3 6 w w w w v dvdw dw =, = : W = 6/3 =.5 =, = : W = 6/ 5 =.3 VarW =.3.5 =.5 =, = : V = 6/ =.75 =, = : V = 6/ 5 =.6 VarV =.6.75 =.375 =, = : WV = 6/3 5 =. CovW, V = =.5 T dia i W + ½ ad ai i V + ½. o dirc bw wo ia i V W or W V. V W = V W =.75.5 =.5 or W V=.5 VarV W = VarV + VarW CovW, V = =.375,,, 6

7 7 Qio 6 i ii iii Tor] [Bioial Var ] [ ] [ ac i a o-graig cio. i L = + +. ic,, ar idpd [ ar], Ti i o-graig cio o Bi, diribio. ig iq ropr o o-graig cio, [ ar] ~ Bi,. T Cral Lii Tor: ppo a,..., i a qc o idpd ad idicall-diribd rado variabl, ac wi ii pcd val ad ii variac. or icil larg val o, l approia ~ N, i i [Giv ar or corrc a i r o.] I co o par ii, = θ ad = θ θ ig rl provd i i. o approial, or larg og, ~ N, approial or, N ~ approial. I wa provd i ii a ~ Bi,. Tror, Bi, diribio ca b approiad b -, N diribio or larg og.,,

8 Qio 7 a i T Tabl providd giv ollowig claiv probabilii [alo giv i ar i cadida wor o poi probabilii ad o calcla corrc claiv probabilii]: =.885, o = =.96, o = 3 =.737, o 3 = 3 =.938, o = 5,, T pdo-rado varia ar,, 3 ad ii d 3, o 3 log =.885, o = 3.9 =.96, o = =.737, o 3 = 3.3 =.938, o = 3.79, ½, ½ ½, ½ b T pdo-rado varia ar 3.9, 3.53, 3.3, or ll abl o rl, pag. [Giv ar or appig i dir digi o poibl oco o di, ar or dicardig all occrrc o or or digi, ar or o arig ill ir 6, ar or applig or codiio. I a cadida carrig o corrc gral procdr a ior rror, ddc ar.] Ti ilaio rqird 58 rado digi, givig 33 valid roll o a di. Rpa ilaio a i poibl or. Co br o roll o di rqird ac i. Obai a appropria irval bad o diribio o br o roll rqird or apl, a +/-.96.d., or.5 o 97.5 prcil o apl diribio., 8

9 Qio 7 # Digi Oco # Digi Oco 5-3 No Roll - 3 No Roll No Roll 3 Aa 5 9 No Roll No Roll No Roll 37 Aa 8 9 No Roll 38 No Roll 9 6 Bod No Roll 8 No Roll 6-7 No Roll 8 No Roll No Roll 3 No Roll No Roll No Roll 5 9 No Roll 6 8 No Roll 6 9 No Roll Lg 8 7 No Roll Tail No Roll 5 3 Lg No Roll 53 9 No Roll Had Lg No Roll Lg 3 9 No Roll 9

10 Qio 8 i, V a, V, J V V ii iii Hc, o rag pac {, v: ; v }, g, v, v v v v v T joi p.d.. acori a prodc o a cio o alo ad a cio o v alo. Tir joi rag pac i a Caria prodc or rcaglar pac. ig acoriaio Tor, ror, ad V ar idpd. T argial p.d.. ar g, o g,, i.. ~ B +, [Giv ll ar o a cadida wo carri o la wo p i rvr ordr.] ad gv v v, v o g v v v, v, i.. V ~ B, [Giv ll ar o a cadida wo carri o la wo p i rvr ordr.] =, o ~ B, + ~ B, + ad Z ~ B, +, b r,

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