Bharathiar University 2006 B.Sc Computer Science Statistics for Mathematics - Question Paper
B.Sc Degree
5, If two dice are thrown, then the number of points ill the sample space are
(a) 12 (b) 36
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{&) 12 () 36
6. Two random variables X and Y are said to be independent if
(a) E(XY) = l
(b) E(XY) = E(X)E(Y)
(c) E(XY) = 0
(d) E(XY) = a constant value.
IIjot pre#sri_.tb LorrfSlsar X iDrpptb Y <sr>pQujiri|p ffrrtruiiip leirfisar srefls},
(5) E(XY) = 1
{) E{XY) = E(X)B(Y)
(it) E(XY) = p0 ||lse) crisifT.
7, The moment generating function of binomial distribution is
(a) (q + pel }'"** (b) (q + pe()
(c) iq + pe"4) (d) (q + petT.
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(*M) (q + pef11 (dg>) iq + pel)
i&) (q + pe~*) (ff) (q + pet)n.
8, For a normal curve, Q.D, M,D, and S.D. are in the ratio
(a) 5:6:7 (b) 10: 12 : 15
(c) 2:3:4 (d) 15 : 12 : 10.
Juj)J|e0a> 6UTsusiruSld), Q.D, M.D. ujjipib S,D. @sif)|ie!T gi Smirmmi
(@) 2:3:4 (ff) 15 : 12 : 10,
15. (a) Obtain the variance of an unbiased estimate os' the population mean under simple random sampling without replacement.
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(b) Define '-statistic. Also obtain its mean.
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SECTION C (5 x 8 = 40 marks)
Answer ALL the questions,
16 (a) What are the characteristics of a good measure of Central Tendency?
Cb) Define Skewness and Kurtosis.
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(c) The scores of two batsman A and B in lea innings during a certain season are given in the following data. Find which of the two batsman A or B is more consistent in scoring ;
A ; 32 28 47 63 71 39 10 60 96 14 B : 19 31 48 53 67 90 10 62 40 80
(|) A tiifppdh B MsQsl.
10 ilurwaar <i<3y> pjui
gaiifl iurrrr t1i|i jSteaHJLj iTanu5u_ju.UJ6u!T cvr ta
A i 32 28 47 63 71 39 10 60 96 14 B ; 19 31 48 53 67 90 10 62 40 80
17. (a) Prove that -1 < r < +1.
(b) State all the properties of regression coefficients,
(<3>i ) -1 < r < +1 ffwuefts jSptfs,
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ikglS.
. Or
11 2615
20. Ca) Derive the expression for
V {yu) cs? Qiri_eD!r sfilsaiuj,
(b) Obtain the MC.F v2 distribution.
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14 2815
Reg, No.:..............................
(For the candidates admitted from 2004 onwards)
B.Sc, DEGREE EXAMINATION, APRIL 2006. First/Third Semester Part III Statistics Allied STATISTICS FOR MATHEMATICS I Time : Three hours Maximum : 75 marks
SECTION A (10 x 1 = 10 marks)
Answer ALL questions.
Choose the correct answer :
I. The correct relationship between A.M., G.M. and
(a) AM = GM = HM
Cb) GM > AM > HM
(c) HM > GM > AM
A.M., G :-l n.mir, H.M.
ifikjfTr g_|pLj(y >>'}> itrjji-y
(.si) AM = GM = HM ;i GM > AM > HM
HM > GM k AM (ff) AM > GM > HM.
2. Formula for loefflcient uf variation s
(a) C.V, = x 100
C.V. = x 100
S.D
Mean x S.D
(c.)
Jldu eha>mo
(*m) LDIT.Q*(lp ;
Alt.i e9a>stb CS) ujit.Qbqp = #ffrffiflx1ilLi?aitb
JiSFif X $.l_ sflfioisib
2
3. The normal equations for fitting a = *r'.t
the forni y-a+bx are
lili"1 <*f
Zy =n-a+bZx 2a - *>
(a) J , , (b) '
Xxy = a2x + 6Sa:" I, - T 1 ,-62x
, , 3y = aZ*+dx8 ,JX t\*3+blx
(c) ' (d)
Z,Tj = -c+62*r Zw 7 b+alx,
y=a+bx STfisrjp CI|5irCS*fnl.fiS onL Qurr(rfj0pQ.is*frr @iub0ns> iDiror r -e r
Ey = n. * a + b Hx , Sy = alie + a I
rL)
Iay=aYx+blx2 ' Lsy = a22+6S*
Zy = a&+te2 ax2+6Sx
(ff)
Zxj = -a + 6Xx N - ' b + al..
4, If 6yx = 0,3 and fey = 1.2, tbeii the valu o
r s
(a) r = 0.6 (b) r = -0.6
<c) r = 0,88 (d) r = -0,36,
byx =0,3 ujjDptb bxy =1,2 r ~
(Km) r = 0.6 () r = -0,6
) r = 0.36 (ft-) r = -0.36.
3
2615
9. The number of possible samples of size two from a population of 4 units is
(a) 2 (b) 4
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{) 2 (<j&) 4
10. The range of F-variate is
(a) co to ao (b) 0 to 1
(c) 0 to oo (d) - oo to 0.
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{) Oto 3 (ff) 00 to 0,
SECTION B (5 x 5 = 25 marks)
Answer ALL the questions.
11. (a) Define Mean, Also mention its merits and demerits.
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Or
(b) Calculate standard deviation from the following data :
Classes : 0-10 10-20 20-30 80-40
Frequency 5 8 7 12
Classes: 40-50 50-60 60-70 70-30
Frequency: 28 20 10 10
gfiaip'tEissftcfiiisip <ltLL_ rftosaib rssbr ;
iSlflajsdr: 0-10 10-20 20-80 80-40
xa>Qajr: 5 g 7 12
i9ifidr 40-50 50-60 60-70 70-80
Jaiafer: 28 20 10 10
7 2615
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