Madurai Kamraj University (MKU) 2007 B.Sc Mathematics maths - exam paper
(8 pages)
6249/M22 october 2007
Paper IV STATISTICS
(For those who joined in July 2003 and afterwards) Time : Three hours Maximum : 100 marks
SECTION A (8 x 5 = 40 marks)
Answer any EIGHT questions
1. ft (oT6OTT(SCTfl6ffr jlsiOfT) cHp)<3j CTSsfld),
aul rflenjpff ffijnffiflaouja ffiSHrglLSIu)..
Find the weighted arithmetic mean of first n natural numbers whose weights are equal to the corresponding numbers.
2. 6J)LDlLIS;i6BT LD(Tp68)Dff ffrTITI5<>5g| SOfiU CTsingjiii), ssTrreb srTaSlsjr LDrrpaneuu Qurrpdggjj sdldilild erafipLD (00iSl.
Prove that standard deviation in independent of change of origin and in dependent on change of scale.
3. 60 Gr5rr<ffiGffifTtliS5)L_ rlp6L|6urr)@ifliu ffiDajTurrglaanen'a sawrQiSlnf.
Find the normal equations for fitting a straight
line.
4. LDrrrfjlGTfl65T Gls;rn_rrL|.$ 2_jD6i|< @5Tffina5 cfili_0SS)jB|Bg] ebsu ctsst tiltSl.
Prove that arithmetic mean of the regression coefficients is not less than the correlation coefficient.
5. C70+l/8=80;C71+C77=10;t7'2+r/6=5 ;U3+U5= 10;
CT(o5fl<oU, U4 -65T LOlumJ<S Srr6WT<K.
If U0 +U8 =80 ; t/1 + C/7= 10 ; U2+U6= 5 and C/3 +t/5 =10, find U4.
6. n uemq&eiflm, Grsfr r)Lpsj<Ka| jg)em&,dil6m Qldit35 OTfi55re5fl<50n<s5)UJ arrewTffi.
Given n attributes, find the total number of positive class frequencies.
7. ffirreoQrri_(fleeT Gurr-sans iliiraruSl0ib stt6l|
Gffinebasn' ujrraoeu?
What are the measurement of trends in time
series?
8. QrTurrffliLifbn) ffiflffLO LnrnfjluSlsijr ffmTL|
f{x)=c\ ;x = l,2,3,..... isrssfld), c crarrD mrnfilaSluSliSOT
\3/
LDluanucS ansrors.
(2\x
If f(x)=c ;x = l,2,3,..... is the p.d.f of a discrete
random variable, find the value of the constant c.
9. rrgi0LJL)u uijguqSIot siLp6U Qu0ffi0ff ffrnianua 6Eftn-(5> lSI iq_.
Find the mgf of the binomial distribution.
10. ggLbugi ansRn-serr Qrr6rori_ $0 ffffisLD inrrlifluSleb, 2_jD6Hffi(g6ff!n\$Lb 0.89 Gresf)), eoeusOT ot@.s<5uul_i_ QrT0UL5l6ST 0.84 CTOTgD 0 (ipU)-U-|LDrr?
In a random sample of 50 pairs of values, the correlation was found to be .89. Is this consistent with the assumption that the correlation in the population is .84?
11. Cjbitgh LDrrdl[fl 2_fDoSl65T
(LpanfD0DlU 6filGU(fl.
Explain the test for significance of observed sample correlation.
12. 51 OTaksroriBjfteTT QsnwL 60 LDrT<lfflu5!sb s = 10 erasfleu, cr=8 crsrrjD GafnlumlanLff
If s = 10 for a random sample of size 51, test the hypothesis <x=8.
Answer any SIX questions.
13. GLp Q<5n@ffi<ULJLl($l6nGrr uijeuGiSleb, ffijrrffif),
1l_I_6lSl60iS<5Lb LDpgy UD g)6OTL> (XCT - ffi@SfT)
0S)6UffianOT ffi6wriSlm..
inluQuaiisr: 10 9 8 7 6 543 21
65)uQeij655T: 1 5 11 15 12 7 3 3 0 1
Find the mean, standard deviation and percentage of class within xa for the following frequency distribution.
Marks 10 9 8 7 6-54321
Frequency 1 5 11 15 12 7 3 3 0 1
14. GLp Gl<35rr<5LJULl(5lsn'STT Li_GLi0O6wruS]isiSl0rBgj, y=abx cramp ajansrraoaj rpeia;.
x: 1951 1952 1953 1954 1955 1956 1957
y: 201 263 314 395 427 504 612
Fit a curve of the form y-abx to the following
data.
x: 1951 1952 1953 1954 1955 1956 1957 y: 201 263 314 395 427 504 612
15. () <517 2-jD64s@iflu-i jglipGn.
(*>) bP eSlJITSlfl65T &JJJIJ(y>Lb otcwl-ilild GlP
Gl<5n'@<KLJUllOT6n'6ffT. )SB)GU(65ffila!)l_Guj 2_STT6rr .glj a_JDCL| gaisrana ffiawrQiSlii)..
2_ujijLb (QmS): 165 167 166 170 169 172 srani- (i!<!): 61 60 63.5 63 61.5 64
(a) Derive the formula for rank correlation.
(b) Find the rank correlation coefficient between the height and weight of 6 soldiers in Indian Army.
Height (cm): 165 167 166 170 169 172 Weight (kg): 61 60 63.5 63 61.5 64
16. (<g{) ffLD lss)L_Qajafl6n' Q<srrOTri_, [ly,LlL_6isT IrflGan-ffl s5)L_ffOff0Q) (gjilijjgans
(b) U15=246, Uao-202 , C/g5 = 118,
Ug0=40 6T0ifla), U19, 5T LDlui_| OT65T6ST?
(a) State and prove Newton - Gregory interpolating formula for equal intervals.
(b) Using it, find U7g, if f/75=246, U80-2Q2 ; U85=118 and Z7go=40.
17. (i) 90 efil(LpL6)uj @r5luSLLQ1_esorewssjyra1 GfftTlijluLb
Lp65Tg)l GffrrsnaiTaansn' oSleuifl.
(<b) Q)ruQuuj(fl6ST @r51iiSLQi_6wr, fii(Lg>uSJuj
@rf)]diLQi_6wr tebeo erm rl0iSI.
5 6249/M22
(a) Explain the three tests for an ideal index number
(b) Prove that Laspeyers index number is not
ideal.
18. (cSj) QuujGfo jflrpai.
(b) $ a:|fl5:LD ldrrrlu51 jt *Lprb Qu0<s0ff ffrnTL| g)0&
Geuemtsj-ujgi <ili_rTUJL> gogd 6T6tlj8>tb(9j f0 2-5,mjmr\i>
Qffirr.
(a) State and prove Bayes theorem
(b) Give an example to show that m.g.f of a random variable may not exist.
19. $Gy> Qffin-ffiuuil($lerTen' acueb (ip6DLb, uijuli (LpanpsinLuu uiuotu!, u-I(dG<kit<o5)6U6)uj jSlpaja. CTlirun-fr<Kuuili_ lffiffiGlGU6wrai)6mL|Lb ffias5TiSliij.. gu@ljl| @5)i_Qsuafl: 60-62 63-65 66-68 69-71 72-74
f: 5 18 42 27 8
Fit a normal curve to the following data by area method and find the expected frequencies.
Class interval: 60-62 63-65 66-68 69-71 72-74
f: 5 18 42 27 8
20. () Quifiuj LD(Tlrfl<56ifleu, i_|sn-6ifliiSlujsb GffimlurrQffiQDefTff Gffrrlr61iL|Lb QpawDanuj oSlerra;*.
(b) 400 Guit QsrTsferL 60 larrlifluSleiT ffijiTffifl 67.47 craiflgo, Lorrlif), ffijrrffif) 67.39, lLi_aSla),sLb 1.3
Qrr655n_ Glrr@LJiSl0Sl0i6gl OT<5uuili_rr?
(a) Explain the procedure for testing of a statistical hypothesis (large samples).
(b) A sample of 400 individuals is found to have a mean of 67.47. Can it be reasonably regarded a sample from a population with mean 67.39 and S.D. 1.3?
21. jgjljsror LDIT|]lf)<C!fl65r (Lpm.66TT ilGLp
Qffin@uuu.srTsn'eifr. gidgu 6Gg- iujb(oln-0LJiSleS)0fBgi
CT@ffiuuili_0najujrr crasrp Gffrrlrl.
Size Sample Mean Sum of squares of deviations form
the mean
Sample 1: 10 15 90
Sample II: 12 14 108
Two random samples gave the following results. Test whether the samples could have come from the same normal population
Size Sample Mean Sum of squares of deviations form
the mean
Sample 1: 10 15 90
Sample II: 12 14 108
22. HGy) QrT@(SuuL_@isiT6tT G60L-U|_6isT idi_(jIq) s_otot LDiTpurTLanu ijrruja;.
A8 C18 B9
C9 B18 A16
Bll A10 C20
Analyse the variance in the following Latin square.
A8 C18 B9
C9 B18 A16
Bll AlO C20
8 6249/M22
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