Exam Details
| Subject | statistics | |
| Paper | paper 2 | |
| Exam / Course | indian forest service | |
| Department | ||
| Organization | union public service commission | |
| Position | ||
| Exam Date | 2015 | |
| City, State | central government, |
Question Paper
STATISTICS
Paper-II
Time Allowed Three Hours
Maximum Marks 200 I
QUESTION PAPER SPECIFIC INSTRUCTIONS
Please read each of the following instructions care/ ully before attempting questions There are EIGHT questions in all, out of which FWE 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 he 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 All questions carry equal marks. The number of marks carried by a question/part is indicated against ii. 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.
SECTION-A
Q .1 Answer all of the following :8XS=40
Q. Explain the theoretical basis of control charts.
Q. Explain the construction of control charts for number of defectives and fraction defective for detecting lack of control in a continuous flow of manufactured products.
Q. Describe single and double sampling inspection plans for attributes.
Q. Obtain the steady state waiting distribution for queue.
Q. Show that a Markov chain is irreducible if and only if each state can be reached from every other state.
Q. Obtain Wald's SPRT of strength (alfa, beta) for testing H0:p Po against H1 p p1 fof'1he ....-i.
distribution
px x 1
0 otherwise. 15
Q. Write notes on the following
AOQ
AOQL
Dodge-Roming Tables. 5x3=15
· Q. A manufacturing company has a certain piece of equipment that is inspected at the end
of each day and classified as just overhauled, good, fair or inoperative. If the item is
inoperative it is overhauled, a procedure that talces one day. Let us denote the four
classifications as states 3 and 4 respectively. Assume that the working condition of
the equipment follows a Markov chain with the following transition matrix
Tomorrow
1 2 3 4
1 0 3/4 1/4 0
2 0 1/2 1/2 0
Today
3 0 0 1/2 1/2
4 1 0 0 0
If it costs .. 125.00 to overhaul a machine (including lost time) on the average and
t 75.00 as production lost if a machine is found inoperative. Using the steady-state
probabilities, compute the expected per day cost of maintenance. 10
Q. The following are the means and ranges of 20 samples of size 5 each of length of a
fragmentation bomb base manufactured in a particular war
Group No. Mean Range Group No. Mean Range
1 0.8372 0.010 11 0.8380 0.006
2 0.8324 0.009 12 0.8322 0.002
3 0.8318 0.008 13 0.8356 0.013
4 0.8344 0.004 14 0.8322 0.005
5 0.8346 0.005 15 0.8404 0.008
6 0.8332 0.011 16 0.8372 0.011
7 0.8340 0.009 17 0.8282 0.006
8 0.8344 0.003 18 0.8346 0.006
9 0.8308 0.002 19 0.8360 0.004
10 0.8350 0.006 20 0.8374 0.006
From the data, obtain the control limits for X and R-charts to control the length of bomb
produced in the future.
(For n A2 0.58, 03 0 and 04
2.12) 15
Passengers arriving at a railway reservation office at the rate . of 25 per hour. If the
approximate average time of issuing ticket is 4 minutes, how many counters should be
opened in the least so that the queue does not go on increasing Supposing that the
requisite number of counters are opened, what would be the average waiting time in the
queue and the time in which ticket is obtained 15
Q ..
Explain clearly with suitable examples the different costs that are involved in the inventory
problems. 10
Q.
If the random life time of an item has distribution function what is the mean
remcining life of an item of age x
Find the mean total life time of an item when the distribution function
1 x .. A 0.
Hence show that the mean life time is approximately 2 times the mean life when the
renewal process has been in operation for a long time. 10
Q.
Prove that if the sum of two independent renewal processes is a Poisson process, then
both renewal processes must be Poisson processes. 15
Q.
A dairy firm has three plants located in a state with daily milk production at plant 2
and13 of 1 and 10 million litres respectively. Each day the firm must fulfil the needs
of its four distribution centres 3 and 4 with minimum requirements of 3 and
2 million litres respectively.
Cost in hundreds of rupees of shipping one million litre from each plant to each
distribution centre is given in the following table
Distribution centre
D3 D4
D1 D2
2 3 11
7
P1
Plant
I 0 6 7
5 8 15
P3
9
Find initial basic feasible solution for this problem using
North-West comer rule
Least cost method and
Vogel's approximation method.
SECTION-B
15
Q. 5 Answer all of the following:
Sx5=40
Q.
Q.
Describe Greville's method of constructing abridged life table.
Describe the main sources of demographic data in India.
8
8
Q. Give a brief outline of factor analysis and discuss its importance in psychometric analysis.
Q. Describe the classical linear regression model. If the disturbances are independently and ..
normally distributed, show that the OLS method and the ML method provide identical
estimators for the regression co-efficients. 8
Q.
Briefly describe any two tests for detecting multicollinearity. 8
Q.
Discuss the different methods of determining trend in a time series. What are their relative
merits and demerits 15
Q.
Construct with the help of data given below Fisher's ideal index number and show that
it satisfies the factor reversal test
Estimated total produce in
Commodity Price per quintal in Rs.
quintals by a small factory
2001 2005 2001 200S
Commodity I 71 26 350 312
Commodity II 107 83 200 187
Commodity III 62 48 256
15
Q.
Describe the merits of using standardised rates in place of crude rates. Explain why
would you consider standardised death rates to give a better measure for comparison of
mortality situation of two communities. 10
Q.
Explain different stages of Box Jenkins method of forecasting. 15
Q.
Write note on the following tests for index numbers
Circular test
Time reversal test
Factor reversal test.
5x3=15
Q.
Fill in the blanks in a portion of life table given below
Age in Yean 1 .. eO
dx Px qx LX Tx
4 95,000 500 48,50,300
5 400
Show details of computation. 10
Q.
Explain the different methods of combining and comparing scores in several tests in
psychology. 15 ..
Q .. What do you mean by intelligence quotient Describe the procedure and tests for measuring
intelligence quotient. 15
Q.
Discuss various official statistics of India relating to Industry. IQ
L
Paper-II
Time Allowed Three Hours
Maximum Marks 200 I
QUESTION PAPER SPECIFIC INSTRUCTIONS
Please read each of the following instructions care/ ully before attempting questions There are EIGHT questions in all, out of which FWE 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 he 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 All questions carry equal marks. The number of marks carried by a question/part is indicated against ii. 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.
SECTION-A
Q .1 Answer all of the following :8XS=40
Q. Explain the theoretical basis of control charts.
Q. Explain the construction of control charts for number of defectives and fraction defective for detecting lack of control in a continuous flow of manufactured products.
Q. Describe single and double sampling inspection plans for attributes.
Q. Obtain the steady state waiting distribution for queue.
Q. Show that a Markov chain is irreducible if and only if each state can be reached from every other state.
Q. Obtain Wald's SPRT of strength (alfa, beta) for testing H0:p Po against H1 p p1 fof'1he ....-i.
distribution
px x 1
0 otherwise. 15
Q. Write notes on the following
AOQ
AOQL
Dodge-Roming Tables. 5x3=15
· Q. A manufacturing company has a certain piece of equipment that is inspected at the end
of each day and classified as just overhauled, good, fair or inoperative. If the item is
inoperative it is overhauled, a procedure that talces one day. Let us denote the four
classifications as states 3 and 4 respectively. Assume that the working condition of
the equipment follows a Markov chain with the following transition matrix
Tomorrow
1 2 3 4
1 0 3/4 1/4 0
2 0 1/2 1/2 0
Today
3 0 0 1/2 1/2
4 1 0 0 0
If it costs .. 125.00 to overhaul a machine (including lost time) on the average and
t 75.00 as production lost if a machine is found inoperative. Using the steady-state
probabilities, compute the expected per day cost of maintenance. 10
Q. The following are the means and ranges of 20 samples of size 5 each of length of a
fragmentation bomb base manufactured in a particular war
Group No. Mean Range Group No. Mean Range
1 0.8372 0.010 11 0.8380 0.006
2 0.8324 0.009 12 0.8322 0.002
3 0.8318 0.008 13 0.8356 0.013
4 0.8344 0.004 14 0.8322 0.005
5 0.8346 0.005 15 0.8404 0.008
6 0.8332 0.011 16 0.8372 0.011
7 0.8340 0.009 17 0.8282 0.006
8 0.8344 0.003 18 0.8346 0.006
9 0.8308 0.002 19 0.8360 0.004
10 0.8350 0.006 20 0.8374 0.006
From the data, obtain the control limits for X and R-charts to control the length of bomb
produced in the future.
(For n A2 0.58, 03 0 and 04
2.12) 15
Passengers arriving at a railway reservation office at the rate . of 25 per hour. If the
approximate average time of issuing ticket is 4 minutes, how many counters should be
opened in the least so that the queue does not go on increasing Supposing that the
requisite number of counters are opened, what would be the average waiting time in the
queue and the time in which ticket is obtained 15
Q ..
Explain clearly with suitable examples the different costs that are involved in the inventory
problems. 10
Q.
If the random life time of an item has distribution function what is the mean
remcining life of an item of age x
Find the mean total life time of an item when the distribution function
1 x .. A 0.
Hence show that the mean life time is approximately 2 times the mean life when the
renewal process has been in operation for a long time. 10
Q.
Prove that if the sum of two independent renewal processes is a Poisson process, then
both renewal processes must be Poisson processes. 15
Q.
A dairy firm has three plants located in a state with daily milk production at plant 2
and13 of 1 and 10 million litres respectively. Each day the firm must fulfil the needs
of its four distribution centres 3 and 4 with minimum requirements of 3 and
2 million litres respectively.
Cost in hundreds of rupees of shipping one million litre from each plant to each
distribution centre is given in the following table
Distribution centre
D3 D4
D1 D2
2 3 11
7
P1
Plant
I 0 6 7
5 8 15
P3
9
Find initial basic feasible solution for this problem using
North-West comer rule
Least cost method and
Vogel's approximation method.
SECTION-B
15
Q. 5 Answer all of the following:
Sx5=40
Q.
Q.
Describe Greville's method of constructing abridged life table.
Describe the main sources of demographic data in India.
8
8
Q. Give a brief outline of factor analysis and discuss its importance in psychometric analysis.
Q. Describe the classical linear regression model. If the disturbances are independently and ..
normally distributed, show that the OLS method and the ML method provide identical
estimators for the regression co-efficients. 8
Q.
Briefly describe any two tests for detecting multicollinearity. 8
Q.
Discuss the different methods of determining trend in a time series. What are their relative
merits and demerits 15
Q.
Construct with the help of data given below Fisher's ideal index number and show that
it satisfies the factor reversal test
Estimated total produce in
Commodity Price per quintal in Rs.
quintals by a small factory
2001 2005 2001 200S
Commodity I 71 26 350 312
Commodity II 107 83 200 187
Commodity III 62 48 256
15
Q.
Describe the merits of using standardised rates in place of crude rates. Explain why
would you consider standardised death rates to give a better measure for comparison of
mortality situation of two communities. 10
Q.
Explain different stages of Box Jenkins method of forecasting. 15
Q.
Write note on the following tests for index numbers
Circular test
Time reversal test
Factor reversal test.
5x3=15
Q.
Fill in the blanks in a portion of life table given below
Age in Yean 1 .. eO
dx Px qx LX Tx
4 95,000 500 48,50,300
5 400
Show details of computation. 10
Q.
Explain the different methods of combining and comparing scores in several tests in
psychology. 15 ..
Q .. What do you mean by intelligence quotient Describe the procedure and tests for measuring
intelligence quotient. 15
Q.
Discuss various official statistics of India relating to Industry. IQ
L