Veer Narmad South Gujarat University 2011-2nd Year B.Com Statics -2, ,- , Veer Narmad South University - Question Paper
University: Veer Narmad South Gujarat University
Program Name :Second Year B.Com
Course Name: SB:0411 - Statics Paper-2, 2nd Year B.Com, March-2011, Veer Narmad South Gujarat University.
examination Month and Year: March-2011.
Duration : three hours
Maximum marks:- 70
Attachment :- PDF file containing SB:0411 - Statics Paper-2, March-2011.
SB-0411
Second Year B. Com. Examination March / April - 2011 Statistics : Paper - II
Time : 3 Hours] 00
[Total Marks : 70
""'N Seat No.:
6silq<3i Pi*unkil SnwiA u*
Fillup strictly the details of signs on your answer book.
Name of the Examination :
S. Y. B. COM.
Name of the Subject:
STATISTICS : PAPER - 2
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-Subject Code No. |
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-Section No. (1,2,.....): NIL |
(0 WSll UMdl |M d.
(3) %TlP*l&H Ol-idl VU(l HLHLHL
dlA-tl UMHi WH =*HlHl : *lO
(*0 <H H*URi<>iH *Htell _y-2x + ll = 0 =>Hd x-0.32>> = 12.7 d, * dl
(0 % OlHlfel* %*(Ul >> = lO + lOx dl <llftU *1
*Htei Hiql.
(3) JllH -HSl fclHRl Hia 92, 108, 120 *1
d, dl <11 fcLHl&dl HlHl 5>UHl.
W % HRdl HHH D = 55-2P Hd *
p
S = 20 + Ah dl H'ttR ttHd'leiU'ill HlMl &Hd 5>UHL.
2
(m) % r12 =0.8, r13 =-0.4, r23 =-0.29 dl &Hd LlMl. *
(e) RilOld *l P(jw,w)=-E=Er *
lw +
* (*0 x2 <l-Cl CHII ?HlHl. ailssy. HR5ll*it &fed X2 PUWSI X
(h) n URC-tqiqi LLHL faaRSl ddl HM HH1 d
5HH lOid *l.
U) Hdl<Cl kbH-ft HWWRl t2 1 /! *Ud?H{l HWL=ILIL p fadkd UH d.
* (*l) JllH MRdl 6(Ul aiL-(l <*HU HlUl. ddl *i<Hl=ldl PuWSldl ?Hd foaRSl *iM.
(H) /,' PUWSI Hiql dlL ddl ?Hd faaRSl WWl.
U) HR5ll*it WLiql <H C-t [dUUdl Hil <Wdl dSWddl
%lUdl U&SM %LH*M.cCl.
3 (?H) H'PLdl RUWKl ?HlUl. % e HLLdl \<*UWl
%lM. <lH dl e = l, e>l, e<l *l[H2d S$L.
(H) % HR'j. Mh x = /(P) ?Hd fldl e 6lH dl P-f(P) Hd f(p)
MhI Hia fldl e-1 ?Hd e + i *Ul MH %lWt.
(b) *kh <ttdl x =>HHl HdW4l Hia |<3. Mh 500 + 13x + -2
d. =*Hd cWl HR. Mh 5x = 315-3P &. dl H6t1H d$l Hia keil ?HHl <Hdmi %1&H ? H6t1H d$l H51 5>UHL.
3 (?h) <&Rl 5Ha<a ? WilHl H6t1H d$l HLSdl *Rdl Hiql.
(H) (*l) llHLdl <HW. &.3U.&6 4 $[tlHl(l <d 4.50 HL UH d cHR ddl VlSl 9,000 fe.3ll.(l d 11,000 fe.3ll. UH d. dl aflHLdl Hadl (-H&lWl *M..
p
(0 %. HR. Mh x = 100- 6lH dl ?Hd HR 40 5HH 6lH cHR tflHid *iM.
U) WR Mdl <HW. 0<Hl5lLHl6 22 HL cHR ddl HR
10,000 fe.3ll. 6c(l. WR ddl <HW. 0<Hl5lLH U 30 HL l*il cHR d-(l HR 8,000 fe.3ll. *kft. % HR Mh P = 4abx 6lH dl etlil a ?Hd b *iM. % <HW. &.311.&6 40 HL UH dl HR kc-il 6*1 ?
(?h) ML LsCL-il nail wuqj. d*u mnhz mW.-i h6ti h.4.
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(<h) 4R *UHC-tl Hlfe4l H**(l aifeld ttl*l4l &d HlHl q.HH2 ?LlH\ : | ||||||||||||||||||||||||
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U) (3lLHOi, 2005 %Uj <UftU <1 &4tel > = 224 + 80x + 4x2 d dl OlHLfel* <1 Htal !>LlHl.
H*l<U
(*i) <161SI *[LH<u4l &dl WWl. C161SI *LlH=u4l -*iddH crM &d %LH*M.cCl.
(H) -flat HTO IHOki LsQ. Hia 2003di <v{< (3l3lHPi| d*U <H&4 -ddH crM &d *HU*ihH. S$L. dH'tf 2009dL
<v{ Hia Hiql :
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<v{ |
2003 |
2004 |
2005 |
2006 |
2007 |
|
fcusi (6%hO |
65 |
92 |
132 |
190 |
24 |
(b) 4R41 Hlfedl H**(l aiR q*ffH aifeld *R*l*l4l d <1 dH'tf 5HH$lteK <IHH2 ?LlH\ :
|
<V{ : |
2000 |
01 |
02 |
03 |
04 |
05 |
06 |
07 |
08 |
2009 |
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M.m : |
50 |
52 |
54 |
56 |
60 |
62 |
65 |
70 |
55 |
58 |
(*i) hl4. [*lHddl r4l <*uwu *UHl. % x = au + b *id
_y = cv + d 6lH dl Rillid *1 Is rxy = ruv. ?Hl a, b, c, d HGll $.
(H) 4R41 Hlfecft HL8 VU jc = 50 cHR J 41 &Hd *iPLlSLd *l :
|
X |
y | |
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28.02 |
4.92 | |
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faaRSl |
19.5364 |
1.21 |
U) <H Wi[\d aififl jc *id jdl Hil 5 *id 10 d. d*U
dHdl H.fa.. 2 *id 3 $. %l C/ = 3x + 4_y *id F = 3X-J;
Ah dl rMV 41 &Hd ?LlH\.
M (h) %. r <H &&HHHU Ah dl HdlHl \ -l<r<l- * (<h) ddH qlM H<Si[M Jdl a' H-Cl [HHd&HH Wl'j Y
y / _\
y-y = r-{x-x) ?hh cft.
U) <H OHHd *iHH WlHl x + 2_y - 5 = 0 Hd 2x + 3>>-8 = 0 dH'Y Y 02=12 A.H dl x,y, <y2y Hd rl &Hd *ilA.
(h) % a,6 Hd c -HSL Hd Hiil Ah dl ax + by Hd cy
a-rax + by
V ./
HdLHl. Wl r H x Hd j Hdl &&HHHU d.
<*1 (r12-r13'r23)
12-3 = ~-1--
a 2 1 r23 U) IR&d *iM HHR lOid
r12~r13'r23 Vt1 _ rl23 ) (x _ r223 )
12-3 _
(h) lOid S$L I :
al-23'a2-31_ _ _ w ~ al a2 12-3 wll
(<h) % C-ll ddl H*hM HLHC-iL Ah dl X1 i X2 Hd X, H 6 OHHd&HH HlHl. % Oj = 6, a2 = 8, o3 = 10, r23 = 0.2,
r31 =0.3, r12 =0.35 Ah dl lOid *l
29 23
X, =-X?+-X,
1 128 2 160 3
Instructions : (1) As per the instruction no. 1 of page no. 1.
(2) The figures to the right indicates the full marks of the question.
(3) Graph papers, statistical tables would be supplied on request.
1 Answer the following questions : 10
(1) Two regression equations are y-2x +11 = 0 and 2 x-0.32> = 12.7, then find coefficient of correlation.
(2) If the quarterly trend equation is y = lO + lOx then 1 obtain yearly trend equation.
(3) The seasonal indices of first three quarters are 1 92, 108 and 120, then obtain the seasonal index on
the last quarter.
(4) If the demand law D = 55-2P and the supply function 2
P
is = 20 + , then find market equilibrium price.
(5) If r12 = 0.8, r13 =-0.4, r23 =-0.29 then obtain the value 2 of 723-1
\j77 f~yi
(6) Prove that (3(w, n) = . 2
I m + n
2 (a) Define % ~ variate. Obtain X distribution with 4
certain assumptions.
(b) Prove that the variance of gama distribution with 4 parameter n is double then its mean.
(c) Show that t2 variate with n degree of freedom is 4 distributed as p variate, with 1 and n degree of freedom.
OR
2 (a) Define the first kind of Beta variate, obtain the mean 4 and variance of Beta first kind distribution.
(b) Obtain Snedecore's F-distribution. State its mean and 4 variance.
(c) Explain the method of testing the significance for the 4 difference between the means of two small samples.
Also state the necessary assumptions.
(a) Define the elasticity of demand. If e indicate the 4 elasticity of demand, then interpret e = l,e>l,e<l.
(b) If the demand function is x = f(P) and the elasticity 4 of demand is e, then show that for the function P.f(P)
f(P)
and , the elasticity is e-\ and e + \-
(c) The total cost function to produce x units of a commodity 4
1 _
is 500 + 13x + Its demand function is 5jc = 375-3P-
How many units should be produced to get maximum profit ? Also obtain maximum profit.
(a) What is monopoly ? Obtain the conditions to get the 4 maximum profit in monopoly.
(b) (1) The price of rice is increased from Rs. 4 to Rs. 4.5, 2
then the supply is increased from 9,000 k.g. to 1,100 k.g. then find the elasticity of supply of rice.
P
(2) If the demand function is x = \00~ and the 2 demand is 40 units, then obtain marginal revenue.
(c) When the price of mango is Rs. 22 per k.g. then its 4 demand is 10,000 kg, when its price becomes Rs. 30
per k.g., then its demand becomes 8,000 k.g. If the
demand function is p = yja-bx , then find the constants
a and b. Also estimate the demand when price would be Rs. 40 per k.g.
(a) What is time series ? State the components of time 4 series. Also explain the importance of time series.
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(b) Obtain the seasonal variations by the method of 6 moving average for the following data : | ||||||||||||||||||||||||
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y = 224 + 80x + 4x2 , then obtain quarterly trend equation.
OR
(a) State the main methods to find trend. Explain the 4 method of least squares to find trend.
(b) Fit a straight line equation by the method of least 5 squares by taking 2003 as origin year for the following time series. Also estimate the sales for the year 2009 :
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Year |
2003 |
2004 |
2005 |
2006 |
2007 |
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Sales (in thousand) |
65 |
92 |
132 |
190 |
24 |
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(c) Obtain trend and short term variations by four yearly 3 moving average for the following data : | ||||||||||||||||||||||
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5 (a) Define Karl Pearson's coefficient of correlation r. If 4
x = au + b and y = cv + d then prove that rxy = ruv. Here
a, b, c, d are constants.
(b) Estimate the value of y when x = 50 for the following 4 data :
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r = 0.8 |
(c) The means of two uncorrelated variables x and y are respectively 5 and 10 and S.D.'s are 2 and 3 respectively. If U = 3x + 4y and V = 3x-y then obtain the value
of ruv
OR
(a) If the coefficient of correlation between two variables is r then show that -i<r<l-
(b) Show that the regression equation of y on jt is 4
- ay (
y-y = r(x-x) _
2x + 3y-8 = 0, and <52 = 12, then obtain the values of x, y, a2y and r.
6 (a) If a, b and c are three positive constants then 4
prove that the coefficient of correlation between ax + by
and c is
a-rax + by
a2c2x + b2c2+2abr-cx-cy
where r is coefficient of correlation between jt and y.
(b) In usual notations, prove that
<*i {ri2-rn-r23)
12-3 = ~1--
g2 1 r23
(c) In usual notations prove that
F _ r\2-rl3-r23 12-3
6 (a) Prove that : 6
al-23'a2-31_ _ _ w ~ al a2 12-3 wll
(b) If three variables are measured from their mean 6
then obtain the Regression equation of X1 on X2 and
X3. If Gj=6, g2 = 8, g3 = 10, r23 = 0.2, r31 = 0.3, r12 = 0.35 , then prove that
1 128 2 160 3
SB-0411] 8 [ 1000 ]
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Attachment: |
| Earning: Approval pending. |
