CS (Main) Exam, 2020
URC-B-ST SC
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STATISTIC S (PAPER-II)
IMaximum Marks : 250 I
j Time Allowed : Three Hours
QUESTION PAPER SPECIFIC INSTRUCTIONS
(Please read each of the following instructions carefully before attempting questions)
There are EIGHT questions divided in two Sections and printed both in HINDI and
in ENGLISH.
Candidate has to attempt FIVE questions in all.
Question Nos. 1 and 5 are compulsory and out of the remaining, THREE are to be attempted
choosing at least ONE question from each Section.
The number of marks carried by a question/par t is indicated against it.
Answers must be written in the medium authorized in the Admission Certificate which
must be stated clearly on the cover of this Question-cum -Answer (QCA) Booklet in the
space provided. No marks will be given for answers written in a medium other than the
authorized one.
Wherever any assumptions are made for answering a question, they must be clearly indicated.
Charts/figure s, wherever required, shall be drawn in the space provided for answering the
question itself.
Attempts of questions shall be counted in sequential order. Unless struck off, attempt of a
question shall be counted even if attempted partly. Any page or portion of the page left blank
in the Question-cum -Answer Booklet must be clearly struck off.
URC-B-STS C/49
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1
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~ - A / SECTION-A
l.
(a)
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M "ri:f
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~,
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"tfft'Tim ~ .
•
m?.T ｾ＠
rm q@
ｾ＠
ｾ＠
Define reliability of a system with an example along with the criteria
10
affecting it.
10
Write a note on the characteristi cs of game theory and discuss its limitations.
(c)
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-ij
to~
P!&-1ff!ftsa ｾ＠
ecfit,q-ll C f ) ) ~ ~ I
'SlT!:rT'r-f ｾ＠
cf;J
to
~:
5x1 +6x 2 -x 3 ~3
-2X1 + X2 +4X3 ｾ＠ 4
x 1 -5x 2 +3x 3 ~1
-3x1 -3x 2 + 7x 3
X1,
X2,X3
ｾ＠
6
~0
Define the concept of duality in Linear Programming Problem (LPP). Write down
the dual of the following LPP :
Maximize
Z
= 2x1 + 5x 2 + 6x 3
subject to the constraints
5x1 +6x 2 -x 3 ~3
-2X1 + X2 +4X3 ｾ＠ 4
x 1 - 5x 2 + 3x 3 ｾ＠ 1
-3x1 -3x 2 + 7x 3
X1,
(d)
1fiffl
ｾ＠
oi.fT ｾ＠
Sll~cfidl ~ - i j A
Sll~cfidl ｾ＠
ｾ＠
Examrace
cf;J
ｾ＠
3ITT BR~~-a rn, ｾ＠
~-am jcfi:Sl3-l 50%
URC-B-STS C/49
X2,X3
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6
~0
ｾ＠
10
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m?.T
0~ 1 ｾＬ＠
ffi
ｾＬ＠
~I
P!&-1ff!ftsa ｾ＠
ｾ＠
i :
A
B
A
0·9
O·l
B
0·5
0·5
2
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Discuss Markov chain and transition probability matrix with an example. For
the following transition probability matrix, determine the market share of
brands A and B from period O to 1, when their initial market share breakdown
is 50% :
ｾ＠
m
A
B
A
B
0·9
0·5
0·1
0·5
10
Differentiate between process control and product control with examples.
2.
SIRti:44-t ｾ＠
(a)
ｾｉ＠
t? ~ - ~ ,
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~if,~
SIRti:44-t
ffl-C:~ (mo lfto)
W.JT
qsJ;
10
<t>1
N=l000, n 1 =50, c1 =3, n 2 =100
amc2 =7i, ~~fcfi3Tit l~~~~-mo cfitit1
What are sampling plans? Define consumer's risk, producer's risk and OC
curve. In a double sampling plan with N = 1000, n 1 = 50, c1 = 3, n 2 = 100 and
c 2 = 7, explain how you would draw your conclusion.
i:4(Emticfil ｾ＠
(b)
~~•101cfi Slell!l..q ｾ＠
ｾ＠
ｾ＠
fcl"qe.fl4<11 ｾ＠
ｾ＠
ｾ＠
15
mta ~ I
Obtain reliability and hazard functions of exponential and lognormal
distributions.
15
(c)
ｾ＠
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(~it{_~e) ｾ＠ ｾ＠
10 ~ . ｾ＠
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ｾ＠
p-~ am c-~ cf>1 ffl ~ I f.ii..i~lt-rn
100 ｾ＠ t, . f i t ~ ~ <t>l ｾ＠
＠ｾ
i1 ｾ＠
ｾ＠
i1
cf>1 ｾ＠
W.JT ｾ＠
ｾ＠
1
lft1ijaif . f i t ~ ~ :
2
3
4
5
6
7
8
9
10
What are control charts for attributes? Discuss p and c charts. The following
data refer to number of defectives in 10 samples each of size 100 items.
Construct an appropriate control chart and interpret the control limits :
Sample No.
1
2
3
4
5
6
7
8
9
10
No. of Defectives
4
8
11
3
11
7
7
16
12
6
20
URC-B-STSC/49
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3.
(a)
ｾ＠
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ｾ＠
cfiT
ｾ＠
ｾ＠
ffi ~ I -qi,;{~ -q -qi,;{ cfiTin ｾ＠
"tR ｾｉ＠
ｾ＠
i :
ffl
A
B
C
D
E
ｾ＠
3
2
5
2
4
1
8
0
3
4
9
9
8
3
5
9
1
8
4
5
6
5
2
0
9
1
4
6
3
5
Discuss Assignment Problem. Consider the problem of assigning five jobs to
five persons. The assignment costs are given as follows :
2
4
9
1
A
Person
B
C
D
E
Job
3
8
0
3
4
5
9
1
8
8
3
5
9
4
6
5
2
2
0
9
5
1
4
6
3
5
15
Determine the optimum assignment schedule.
(b)
ｾ＠
f.ti:.iR-t~a ｾ＠
cfiT MODI
ｾ＠
AA ｾ＠
f.tq,1ft.tv_ :
1Rfoll
Di
ｾ＠
02
03
"IWT
D1
D2
D3
D4
'JITCl1ffl
1
3
4
20
2
1
2
5
30
4
1
9
10
30
50
20
3
2
40
Solve the following Transportation Problem by MODI method :
Destination
Di
Origm
02
03
Demand
D3
D4
2
1
3
2
40
2
5
30
4
1
D1
D2
1
3
4
20
9
Availability
30
50
20
10
15
URC-B-STSC/49
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mlfP:f ｾ＠
(c)
-w.JllR ｾ＠
cf?t ｾ＠
~ I f.li:.i~f©a ｾ＠
-w.11lR ｾ＠
Cf>T ｾ＠
ｾ＠
cf?t
fitll-Mfcntf~~:
-i._•ldiflcfi(UI Z
= 2x1 + x 2
ｾ＠
3X1 +X2 =3
4x1 +3x 2 ｾ＠ 6
X1 +2X2
x1
~o.
x2
S:3
~o
Explain the general Linear Programming Problem. Solve the following LPP by
Charnes' Big-M method :
Minimize Z
= 2x1 + x 2
subject to the constraints
3X1 +X2 =3
4X1 +3x2 ~6
X1 +2X2
x1
ｾＭ＠
4. (a)
1pl'-~ ｾ＠
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~3
~o. x 2 ~o
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20
ｾ＠
<t>l ｾ＠
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1
~A
I
II
m
w
2
5
6
3
5
8
7
4
2
~B
3
4
3
9
8
4
9
7
8
5
f.li.:t~f©a ｾ＠
<t>l
5
6
8
7
3
Define two-person zero-sum game and saddle point of a payoff matrix. Solve
the following game :
Player A
I
II
m
w
2
5
6
1
3
5
8
4
7
2
Player B
3
4
4
9
3
7
9
8
8
5
5
6
8
7
3
15
(b)
ｾ＠
3Titl~~t? ｾｴ＿＠
M/M/1 ~cfit~aTICf>Tffl ~l
What do you understand by queuing theory? What are its advantages? Discuss
the characteristics of M/M/1 model.
URC-B-STSC/49
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(c)
m it M
l.Hil'il'"4
t,
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l{1U{
filq:i(.-lol ｾｉ＠
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t? (Sl<-ll'il'"4 ｾ＠
lfR1
t I ｾ＠
20 ｾ＠
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W-n ｾ＠
100 ｾ＠
SIIRl<tiol ｾ＠
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m"{Ufi yg "({o 9
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cf;T
-if~~ t)
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M
ｾ＠
cf;T
cfiJl--«-cfiJl
ｾ＠
5H-1i'i1'"4
m,
130 ｾ＠
Derive failure rate of a device assuming normal distribution. Suppose the life of
an equipment is known to be normally distributed with mean 100 hours and
standard deviation 20 hours. What is the probability that the equipment would
last at least 130 hours? (Normal Distribution Table is given in Page No. 9) 20
~ B / SECTION-B
5.
(a)
M "CR\~ cfi1 ,at«fl cfil
fi<fi~-11 "<fiT ｾ＠
,at«n ｾ＠
~I
"5lcfiTU cfi1 ｾｉ＠
ｾ＠
10
Explain the concept of validity of a test. Describe various types of validity.
(b)
ｾ＠
qi@
ｾ＠
"<fiT
cf;T
ｾＭ＠
W-n ｾ＠
-qft\ffl'ffi ~ I ｾ＠
qi@
ｾ＠
ｾ＠
it fcNc; ~ I ｾ＠
ｾ＠
qi@
"3Gmul ~ I
Define time series. Distinguish between stationary and non-stationa ry time
series. Give an example of stationary and non-stationa ry time series.
Rl-i:i<HR ｾ＠
(c)
ｾ＠
cf;T
ｾ＠
ｾ＠
ｾ＠
qUR ~ I
10
Discuss variate difference method with an application.
ｾ＠
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(d)
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t? ｾ＠
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~ I ｾ＠
G< "<fiT ｾ＠
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G( i t ~ ~
ｾ＠
G11n
t?
m, err~~
G< .f;t
＠ｾ
-q;) ~ 1
Define Crude Death Rate. Write its merits and demerits. Generally, what is the
range of Crude Death Rate? Is there any relation between female CDR and
male CDR? If yes, then state the relation.
Pti:.i~f&o
(e)
ｾ＠
~-« WRJ ~-G< ｾ＠
R-i•llj41ct 105 ｾ＠
aey
(<ffl it)
URC-B-STS C/49
Examrace
"4< 100 ｾ＠
10
f.rc@ ~-G< cf;T ｾ＠
~'
~ff~ fcn ｾ＠
10
ｾ＠
t:
aey-f.im ~-c:f
.,qllm"{flft
"filTcR w';l'fi(9((1
15-19
0·0696
4180
20-24
0·2346
4123
25-29
0·1897
4063
30-34
0·1143
4001
35-39
0·0611
3934
40-44
0·0285
3860
45-49
0·0101
3763
6
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Calculate gross and net reproduction rates from the following data considering
sex ratio at birth to be 105 males to 100 females :
Age
(in years)
Age-Specific
Fertility Rate
Female Life Table
Stationary Population
15-19
0 ·0696
4180
20--24
0 ·2346
4123
25-29
0·1897
4063
30--34
0 ·1143
4001
35-39
0 ·0611
3934
40--44
0·0285
3860
45-49
0 ·0101
3763
10
6.
ｾｴ＿＠
(a)
1 1 ; c f l ~ • eq$11~Q,l
~tmuRTT~~cfilfl~s fiJl~cfil
ｾｉ＠
What is the problem of identification? Explain it with the help of an example.
Establish rank and order conditions of identifiability.
(b)
-qcn qil sfiJI,
ｾｗｕ＠
~ c f ; ' @ ~ qiJ &l-41~~-l
ARIMA ｾ＠
"Q
15
m, 3Wf
~Wo~, 1t~-ijffi~I
Explain in brief how you will determine orders of autoregressive and moving
15
average terms while fitting time series using ARIMA modelling.
fcJ
(~o v:q;o) "CR\~ ｾ＠
ｾＭ＠
t? ｾ＠
ｾ＠
fcfi
3Wf ｾ＠
"CR\~ qiJ
m M
cft ｾ＠
cf;'@
~cf;\ ~1cm11~"CR\~~~~~ 1
What is Dickey-Fuller (DF) test? Describe how you will use this test for testing
20
stationarity of any given time series.
7.
(a)
11;cf) ｾ＠
m"{Ufi ｾ＠
ｾ＠
ｾ＠
11;cfl ｾ＠
ｾ＠
ｾ＠
~lijlJf
m~ ｾ＠
ｾ＠
"enuft -ij ｾ＠
46 qi{ ｾ＠
-ij 45 qi{ ｾ＠
ｾ＠
-q-c:1 qiJ cf1JR ｾ＠
I qlJ m"{Ufi -ij ｾ＠
~ : 30450 WU 30320
el;) ｾ＠
t
I
I
q45qil~~I
Differentiate between a complete life table and an abridged life table. Explain
the terms involved in life table. In a sample survey of a locality, the number of
15
males of ages 45 and 46 were 30450 and 30320 respectively. Calculate q 45 .
(b)
ｾ＠
'iH-~ cfsfi el;) fcmm: "Q ｾ＠
3llt ｾ＠
ｾ＠
31-414')1~-l
el;)~ eq$ll~Q,1
Discuss in detail Gompertz curve for population growth and explain the
15
method of its fitting.
URC-B-STSC/49
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tR\~ -qm
(c)
ｾ＠
eq$11~Q,I ｾ＠
q1qst,qo1 ｾ＠
ｾ＠
11,qi ｾ＠
am ｾ＠
ｾ＠
~? <Jiffil'TR ~ , lfRcti ｾ＠
ｾ＠
T ｾ＠
ｾ＠
~?
ｾ＠
~q~Rc41~ ~ , ｾ＠
ｾ＠
86 ｾ＠
ｾ＠
ｾ＠
15 t, it Wf
3ffi ｾ＠
ｾ＠ ｾ＠
"sfilm: 91 3ffi 83 ｾ＠ I "ff <fiffil'TR ＠ｾ
cf;) lfRcti ｾ＠
it ｾ＠
~ ' ｾ＠ ｾ＠
500 ｾ＠
lfRcti ｾ＠
100 I
What do you understand by scaling of test items? What are raw scores,
standard scores and T scores? Explain. In a behavioural study on a group of
students with mean 86 and standard deviation 15, Ram scored 91 and Shyarn
scored 83. Express these raw scores as standard scores with mean 500 and
standard deviation 100.
20
t
8.
ｾ＠
(a)
＠ｾ
ｾ＠
qif &1li.fi(1cfil ij?.{J ｾ＠
ii
il~tR&dl ｾ＠
ｾ＠
1R ｾ＠
{1/.fi~-11 "cfiT
cf1lR ｾ＠
I am ｾ＠ ｾ＠
ｾ＠
~? llllmUT ｾ＠
11~ 'cfi7 eq$11~1.t1
Explain the concept of multicollinearity in general linear model. How will you
detect it? Discuss its impact on OLS estimators and their variances.
~-1e~1 ｾ＠
(b)
1R ｾ＠
ｾ＠
"cfiT
ｾ＠
ｾ＠
"qsfi
'cfi7 eq$11~((1 M v_q; ｾ＠
rn ｾ＠
"qsfi
ｾ＠
~-1e~1 ｾ＠
cf1lR ~ ,
Explain logistic curve for population projection. Describe any one method for
fitting logistic curve to the population data.
ｾ＠
(c)
ｾ＠
ei~c#i'I
ｾ＠
ffl ｾ＠
15
cfill4i(1l4 (lfio ~o 3110) ｾｩｴ＠
ｾ＠
ｾ＠
ei~c#i'I
15
f.l~llllW~
~? fclifdR'(4i.fi eq$11~1.{I
What are the main functions of Central Statistics Office (CSO) and Directorate
of Economics and Statistics established in different States? Explain in detail.
20
***
URC-B-STSC/49
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ｾ＠
: ｾ＠
SH-I Iii 1-4 ｾ＠
Table : Cumulative Normal Distribution
cj)(x)
= Jx
_l_e-t2 /2dt
--5,
·00
·01
·02
·03
·04
·07
·08
·09
·2
·3
·4
·5040
·5438
·5832
·6217
·6591
·5080
·5478
·5871
·6255
·6628
·5120
·5517
·5910
·6293
·6664
·5160
·5557
·5948
·6331
·6700
·05
·5199
·5596
·5987
·6368
·6736
·06
·5000
·5398
·5793
·6179
·6554
·5239
·5636
·6026
·6406
·6772
·5279
·5675
·6064
·6443
·6808
·5319
·5714
·6103
·6480
·6844
·5359
·5753
·6141
·6517
·6879
·5
·6
·7
·8
·9
·6915
·7257
·7580
·7881
·8159
·6950
·7291
·7611
·7910
·8186
·6985
·7324
·7642
·7939
·8212
·7019
·7357
·7673
·7967
·8238
·7054
·7389
·7704
·7995
·8264
·7088
·7422
·7734
·8023
·8289
·7123
·7454
·7764
·8051
·8315
·7157
·7486
·7794
·8078
·8340
·7190
·7517
·7823
·8106
·8365
·7224
·7549
·7852
·8133
·8389
1·0
1·1
1·2
1·3
1·4
·8413
·8643
·8849
·9032
·9192
·8438
·8665
·8869
·9049
·9207
·8461
·8686
·8888
·9066
·9222
·8485
·8708
·8907
·9082
·9236
·8508
·8729
·8925
·9099
·9251
·8531
·8749
·8944
·9115
·9265
·8554
·8770
·8962
·9131
·9279
·8577
·8790
·8980
·9147
·9292
·8599
·8810
·8997
·9162
·9306
·8621
·8830
·9015
·9177
·9319
1·5
1·6
1·7
1·8
1·9
·9332
·9452
·9554
·9641
·9713
·9345
·9463
·9564
·9649
·9719
·9357
·9474
·9573
·9656
·9726
·9370
·9484
·9582
·9664
·9732
·9382
·9495
·9591
·9671
·9738
·9394
·9505
·9599
·9678
·9744
·9406
·9515
·9608
·9686
·9750
·9418
·9525
·9616
·9693
·9756
·9429
·9535
·9625
·9699
·9761
·9441
·9545
·9633
·9706
·9767
2·0
2·1
2·2
2·3
2·4
·9772
·9821
·9861
·9893
·9918
·9778
·9826
·9864
·9896
·9920
·9783
·9830
·9868
·9898
·9922
·9788
·9834
·9871
·9901
·9925
·9793
·9838
·9875
·9904
·9927
·9798
·9842
·9878
·9906
·9929
·9803
·9846
·9881
·9909
·9931
·9808
·9850
·9884
·9911
·9932
·9812
·9854
·9887
·9913
·9934
·9817
·9857
·9890
·9916
·9936
2 ·5
2·6
2·7
2·8
2·9
·9938
·9953
- ·9965
·9974
·9981
·9940
·9955
·9966
·9975
·9982
·9941
·9956
·9967
·9976
·9982
·9943
·9957
·9968
·9977
·9983
·9945
·9959
·9969
·9977
·9984
·9946
·9960
·9970
·9978
·9984
·9948
·9961
·9971
·9979
·9985
·9949
·9962
·9972
·9979
·9985
·9951
·9963
·9973
·9980
·9986
·9952
·9964
·9974
·9981
·9986
3·0
3·1
3·2
3·3
3·4
·9987
·9990
·9993
·9995
·9997
·9987
·9991
·9993
·9995
·9997
·9987
·9991
·9994
·9995
·9997
·9988
·9991
·9994
·9996
·99 9 7
·9988
·9992
·9994
·9996
·9997
·9989
·9992
·9994
·9996
·9997
·9989
·9992
·9994
·9996
·9997
·9989
·9992
·9995
·9996
·9997
·9990
·9993
·9995
·9996
·9997
·9990
·9993
·9995
·9997
·9998
1·645
·95
·10
1·960
·975
X
·O
·l
X
cl>(x)
2(1- ci>(x ))
1·282
·90
·20
URC-B-STSC/49
Examrace
·OS
2·326
·99
·02
2·576
·995
·01
9
3·090
·999
·002
3·291
·9995
·001
3·891
·99995
·0001
4·417
·999995
·000001
21B8-36
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Examrace
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