Veer Narmad South Gujarat University 2010 M.Com Commerce Advaced Statistics : - III, ( Part - I ) - - Question Paper

RE-3369

M. Com. (Part - I) Examination April/May - 2010 Advanced Statistics - III

Time : 3 Hours] 00

6silq<3i Puunkiufl SnwiA u* qsq d-onql. Fillup strictly the details of signs on your answer book.

Name of the Examination :

M. COM. - 1

Name of the Subject:

ADVANCED STATISTICS - 3

-Section No. (1,2,.....): NIL

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M*l<U

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(h) mnfah ML [u_t : t = 1, 2,............} HVfl JllH GHHd

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b    c-u d. hia(%$    e_t hiMI HR5u*it

UHL'SL d :

(e,) = 0, ) = V(_e() = y(_E() = a²,i = l,2,........

(e,,e;) = 0, (#i' = l,2,........., V₀=0,|o|<l

dl WR i -> oo Ah cHR lOid S$L I lim p_fe = a^k

t>oo

* (*i) *iid*    *lael ? OHHd *i<HH    

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et&t HIHHIHI *imi d. iidHHd eflft ddH =l³Ml &d (3UH>(1 H(l d %LH*M.cCl.

(*l) PlHH faaRSldl %LH*M.cCl.    Ut    H=td d. d H&SM S*<U Hiai Md <il2%H H&SM %LH*M.cCl.

(h) % *t4tel U_t+2 + aU_t+1+bU_t = e_t+2 6RI cHllfad Mh u4l OHnd&HH slstki h141 %Lu Hil *M Ah dl lOid %

v(u_t) i+b

V(_El)"(i-6){(o-6)²-o²}

WU

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u_t = pu_t+l = n_t Hia lOid s$l I p_k=p^k Wl n_t H

Hmill Hia aiL d 5Hd #(,n = 0 (i * j) ?Hd Pfe> k - &Hdl    d.

(H) *t4tel C/_i+2 + at/_f+1 + bU_f = E_t+2 6RI cHLlPld fe4h

ll4l GHHd iHH ?>Rul a ?Hd b 41 &Hd slstkd

HHiildi 3HHL Hiql. dH'tf *U IMh ll4l **[4Hd HH stetkl -LsCLld    r, =0-6 *id r₂ = -0 15 6lH dl

*Rlil a *id 6 41 &Hd ?LlH\.

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(l) g = +l)a(jc₂ + l)P, a>0, (3>0, A>0

(*) g = 100 (x₁ +x₂) + 20x2 -12.5 |x +%2 j, %i > 0, x₂ > 0

*l*l<U

(m) %    Mi Hiai    Mh U = 4SL + L_y-L²

6lH dl 3ll6idl ilH HIS .q.61 Mh HWl.

(H) GcUlkd Mh q = 10 -Xj¹ -x¹ Hia OH&U x_x Md JC₂ HI

MiH&6 &Hd 73, = 4 Md p₂ = 1 &. % HI MiH&6 &Hd p = g 6lH dl Gc'Hlkddl H6t1H d$l 5>llHl.

(m) *1 <Ml i    Mh [7(x + 2)²/3(j' + 1)^1/3 6.

HliL 2jc + 3/ = 7 6. dl d[]M Mh H6t1H Hd d HlSdl

X Md BrHdl *iWl.

(h) M*ll M UWl Mh (CES) SlHWiL. CES GcUlkd [cLHdl LHHl %LH*M.cCl.

M*l<U

(m) <H <MVti mi X_} Md x₂ HIS 2ll6i d[]M Mh / = alog+ 2) + |31og (+&) &. dl <Hd Ml

6aX| + a(3x₂

M-ft *UWl ^{= 1+}/ _xR\- & dH Hdl<Ct.

(a + p j

(h) <H Ml x_x Md x₂*i tj.[p Mh U = Jx_]x₂ &. %

'Wl .r, Md JC₂ -ft MiH&6 &Hd P, = 5 Md P₂ = 2 dl'SlliH MiH 6lH d*U 2U6idl HL HW MWi 100 dl'SlliH MiH dl x_x Md JC₂ HI &Hdl Hiql d*U >,dl &Hd H>SL 5>llHl.

Instructions : (1) As per the instruction no. 1 of page no. 1.

(2) Figures to the right indicate full marks of the question.

1 (a) Obtain korder serial coefficient of correlation for 6 the series A^m e_t, which is obtained by variate difference

method m times for a random series E_t, t = 1,2,........, N

here    = V{e_t = V.

(b) Prove that the constant a and b of second order 8 auto regressive series in the form of serial coefficient of correlation defined by the equation

U_t+2 + aU_t+l + bU_t = E_t+2 are

9

rl -Y.'l    -Y.'l    

1 ^r9 ~ ^ri    r - r₉

^a=Tf ^and b=T[

OR

1 (a) Explain Generalised least square method. Also write 7 the Aitkens theorem.

(b) The first order auto regressive series equation is    7

U_t+1 = aU_t + b + E_t+1, Obtain from the time series

jt/j :t = 1,2,............j, where a and b are real variables

and the assumptions of the error term _t are given below.

'.2\ T7/. \ T7/. \ -2

(e,) = 0, (<) = V(e_f) = V(e₍) = ,t = 1,2, eL, e'_f) = 0, t*t' = 1,2,........., y = 0, \a\ < 1

1 _ k

and when t > > then prove that ^lim Pk~^a .

oo

What is multicolinearity ? The regression equation 8

is y_t = + $2^x2t ⁺ ct where every variable is

measured by taking mean as centre. Explain the method of least squares cannot be useful due to multicolinearity.

Explain the problem of identification with illustration. 6

OR

Explain periodogram. Obtain the relation between    6

periodogram and correlogram.

Obtain korder serial coefficient of correlation for 7 random series    .......^En where Ee_tj =0,

E[e_t, e_s) = 0, t* s . The series n_v n₂...........ⁿn__m+i i^s

obtained with weighted moving average w₂,.......iv_m.

Explain Heteroscedasticity. Explain Durbin-Watson 7 test to examine that there exists auto-correlation between the error terms.

If the term of second order auto-regressive series are 7 very large defined by the equation

U_t+2 + aU_t+l+bU_t = e_t+2 then prove that

v(u.) 1+b

V(e,)^-(1__t){(₀__t)*_₀*}

OR

Explain the difference between cyclical time series    7

and oscillatory times series. Give the causes for the happening of oscillatory time series.

For the autoregressive series U_t = p U_t+l = n_t, prove that = p^k, where n_t is a random variable, with mean

zero and E{x,n = 0 (ij) and Pk is &^th term auto coefficient of correlation.

Obtain the constants a and b of second order auto 7 regressive series in the form of serial coefficient of correlation with is defined by the equation

U_t+2 + aU_t+l+bU_t = e_t+2

and if the coefficient of correlation of auto regressive series are = 0 6 and r₂ = -0 15 then find the value of a and b.

State and prove Euler's theorem.    7

Obtain the marginal rate of input substitution for 7 the following production functions :

(1)    q = +l)a(jc₂ +l)(3, a > 0, (3>0, A>0

(2)    q = 100(x₁ +x₂) + 20x2 -12.5 +x| j, x₁ > 0, x₂ > 0

OR

The utility function for a day is U = 48L + L_y-Lⁱ,    7

then obtain supply function for consumer.

The price per unit of the input and x₂ are p = 4 7

and = 1 for the production function q = 10 - x¹ - x¹

If the price per unit of q is p = q. then obtain the maximum profit for the producer.

5 (a) The utility function for two commodities x and y is 7

U(x + 2)²(y + lf and the budget function is

2x + y = 7, obtained the value of x and y which maximizes the utility function.

(b) Explain the constant elasticity of substitution production 7 function (CES). Explain the properties of the production function (CES).

OR

5 (a) The utility function for the quantity of x and x    8

is U = alog +a) + piog (x_x + &), they show that elasticity of substitution between two commodities is 6olT| + a(3x₂

1 +

(a + (3) x

(b) The utility function at two commodities, x and x 6 is U =    , If the price per unit of the two quantity

x and x₂ are P₁ = 5 and P, = 2, financial unit the capacity for expenditure, revenue is 100 unit then obtain the value of x and x₂, also obtain the value of

RE-3369]    8    [ 200 ]

1

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j(e_r e_s) = 0, t* s) W_VW₂,.......w_m <HRHltl aifeld *R*l*l*(l

m\[ n_vn₂...........ⁿn-m+1 HmiHl d. *U ts(l HL8

k - AH-tl LsCLld    Hiql.

Attachment: veer-narmad-south-gujarat-university-2010-m-com-commerce-29126-1.pdf

Earning:   Approval pending.