UPSC IFS 2017 Question Paper for Statistics Paper-II

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STATISTICS
Paper II

Maximum Marks: 200
lime Allowed: Three Hours

QUESTION PAPER SPECIFIC INSTRUCTIONS

Please read each of the following instructions carefully before attempting questions.

There are EIGHT questions in all, out of which FIVE are to be attempted.
Question Nos. 1 and 5 are compulsory. Out of the remaining SIX questions, THREE are to be
attempted selecting at least ONE question from each of the two Sections A and B.

Attempts of questions shall be counted in sequential order. Unles's stkuck oft 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
All questions carry equal marks. The number of marks carried by a question/part.is indicated
against it.
Answers must be written in ENGLISH only.
Unless otherwise mentioned, symbols and notations have their usual standard meanings.

Assume suitable data, if necessary and indicate the same clearly.

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SECTION 'A'

1. Answer all of the following: 8x5=40
1.(a) Distinguish between tolerance limits and specification limits. Interpret . the situation
when tolerance limits are not included within the specification limits. 8
1.(b) Describe the different types of redundancy and their USCS in reliability
improvement. 8

1.(c) Explain the following terms :
(i) OC function (ii) ATI (iii) AOQL (iv) LTPD

1.(d) Consider the Markov chain with the following transition probability matrix:

0 1 2
00 1 0`
P=1 4 0 T?!--
2\0 1 0

Is the chain irreducible?

Check whether the states of the chain are periodic, persistent and non-null. 8

1.(e) What is a linear programming problem (LPP) ? Differentiate between the simplex
method and two-phase simplex method for solving LPP. 8

Develop the OC function of a double sampling plan for attributes. 10
Distinguish between process control and product control. What are the Statistical
techniques to achieve these? 15
The following data is on minutes to breakdown for an insulating fluid. There were
11 tests at 30 kV. After 100 minutes, there were 7 breakdowns at the following
times in minutes :
7-74, 17-05, 2046,
- 21-02, 22•66,.43•40, 47-30.
The other 4 units had not failed.
Assuming the failure time distribution is exponential calculate the WILE for the
Reliability Function at time t = 25 minutes. 15

3.(a) Use duality to solve the LPP :
Minimize z =3x1 + x2
Subject to 2x 1 + 3x2 2
x I +x2 ?.-
X i , X2 ?- 0. 20

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d's 3.(b) Solve the following transportation problem :

D1 D2 D3 D4 a,
0, 10 7 3 6 3
02 1 6 8 3 5
03 7 4 5 3 7
bj 2 6 4

In a game of matching coins with two players, suppose A wins one unit of value
when there are two heads, wins nothing when there are two tails and looses unit
of value when there is. one head and one tail. DeterMine the pay off matrix and the
optimal strategies for both the players. 20

Solve the following LPP :
Maximize z 2x1 + 3x2 + x3
Subject to —3x1 + 2x2 + 3x3 = 8
—3x1 + 4x2 + 2x3 = 7
x], 20

SECTION 'B'

5. Answer all of the following: 8x5=40

What is homogeneity error in connection with index number? What steps will you
take to reduce this error? 8

Discuss the rationale behind the moving average method in determining trend: 8

What do you mean by parallel tests? Obtain the effect of test length on the
reliability of a test. 8

What are the different components of a time series? Why a multiplicative model
is often preferred for explaining a time series on economic and business data?
8
Define and compare the crude birth rate, gross and net reproduction. rates as
measures of fertility. How do you determine the rate of growth of a population?
8

6.(a) Write down the usefulness of cost of living index number. Can we have a single
cost of living index number for India? Give reasons in favour of your answer.
20

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6.(b) The following table gives (with no missing values) the overall and groupwise cost
of living indices (With the year 2000 as base) with six different expenditure groups
and their respective weights, for the urban middle class people of a particular city,
in 2004 and 2005 :
Group Weight Group Index (2004) Group Index (2005)
Food 350 117 120
Clothing and Footwear 156 113 118
Housing 187 118 —
Transport and Vehicles 108 112 117
Durable household goods 76 102 111
Other items 123 121 125
Total 1000 119-5
Compute the overall cost of living index for 2004.
Hence, determine the group index for housing in the year 2005. 20
In a music competition there are m participants who are to be evaluated by n judges
who want to judge the participants by ordering their performances. Discuss in detail
how can you combine the verdicts of the judges to come to a final conclusion.
Clearly mention the assumptions, if any. 20
Given the following table for Ix, the number of rabbits living at age x, complete the
life table for rabbits :
x 0 1 2 3 4 5 6
c 100 90 80 75 60 30 0

If A, B, C are three rabbits of age 1, 2 and 3 years respectively, find the probability
that
at least one of them will be alive for one year more.
A, B, C will be alive for two years of time.
Exactly one of the three is alive in two years of time.
All will be dead in two years time. 20
8.(a) (i) Which scale is mainly used to measure a Psychological trait?
Suppose you have two score distributions given by

0 x s. and

0 y /2
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for scores x and y respectively. Find the equivalence curve relating x and y and
mention its utility.
Describe in brief, a practical method for obtaining equivalent scores from
the score distributions for x and y without going into the process of graduation.
20
8.(b) Explain multicollinearity with an example. Discuss the different methods of
detection of multicollinearity. 20

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