Exam Details
| Subject | statistics | |
| Paper | paper 2 | |
| Exam / Course | indian forest service | |
| Department | ||
| Organization | union public service commission | |
| Position | ||
| Exam Date | 2014 | |
| City, State | central government, |
Question Paper
SECTION-A
1. Answer the following
Generate 10 randdm numbers from uniform using mixed congruential and multiplicative congruential methods.
Distinguish betwe..n Product control and Process control.
Show that the problem of two-person zero-sum game -can be viewed as a particular case of LPP.
illustrate one application each on MTTF and MTBF.
Describe CUSUM chart and write the procedure of constructing V-mask.
Maximize Z ax 2y subject to
-2x+3y S9
3x-2y S-20
Write the atgdrithm of solving a two-person zero-sum
max min mininax.
Explain the use ofiAOQL and LTPD as a measl,lre for constructing any sampling plan. 10.
Define the following:
Reliability function
Hazard functiod
Reliability of a leries system
Reliability of a ..arallel system
Use of bathtub model
3.(a)Explain the procedure of constructing control chart for fraction defectives and control chart for number of defectives. Also list out the applications for
A company has a demand of 1200 units/year for an item and it can produce 2000 such items per month. The cost of one setup is r 400 and the holding cost/unit/month is 15 paise. Find the following 10
Optimum lot size
Total inventory cost/year assuming the cost of 1 unit as r 4
Maximum inventory
new scooter costs r 6,000. The running cost and salvage (sale price) value at the end of the year are as under
Year 1 2 3 4 5 6 7
Running cost (in dallor)=1,200 1,400 1,600 1,800 2,000 2,400 3,000
Salvage value (in dallor) 4,000 2,666 2,000 1,500 1,000 600 600
If the interest rate is 10% per year and running costs are assumed to have occurred at midyear, find when the scooter should be replaced. 15
Draw a 5-point OC cuive for the single sampling plan
N 1000, n 150 and c 2 Also mention the merits and demerits of single and double sampling plans. 15
A shipping company has a single unloading dock with ships arriving in a Poisson fashion at an average rate of 3 per day. The unloading time distribution for a ship with n unloading crews is found to be exponential with average unloading time fri days. The company has a large labour supply without regular working hours and to avoid long waiting times, the company has a policy of using as many unloading crews as there are ships waiting in line or being unloaded. Find the following 10
Average number of unloading crews working at any time
Probability that 4 crews will be needed
Write on the following 15
Dam models
Transportation problem is a particular case of LPP
Statistical graphs using SPSS
SECTION-B
5. Answer the following::
Sx5=40
The average wage of a· labour worker for a day wast' 255 in 2000 and r 410 in 2014. If the consumer price indexes for these years were 155 and 240 respectively, find, the money wage increase in 2014 compared to 2000.
Define Net Reproduction Rate and Total Fertility Rate and explain their importance. in understanding the growth of a population.
(c)Mention and discpuss a test for homoscedasticity.
Define life table.I Explain various columns of abridged life table and their inter-relationshi s.
Explain the application of chi-square test in psychometry. In a study of 100 voters polled on an issue, sixty voted and forty voted Test the hypothesis that proportion-Pprop 0 · 70.
(Given, the critichl value of chi-square at, 0·5 level is 3·841)
6. Mention underlying assumption of multiple linear regression model. Derive the ordinary least sctuare estimator of the regression parameter in the multiple linear regression model. 15
What· are chain index numbers? How are they constructed?
In the constriU I ction of a certain cost of living index number, the following group index numbers were found. Calculate the cost of living index number by asing the weighted arithmetic mean and also by using the weighted gedmetric mean
proup IndexNumber Weight
Food 350 5
Fuel and lighting200 1
Clothing: 240 1
House: rent 160 1
Miscellancous 250 2
(c)Explain the sampling design and method of estimation for estimating yield estimation of major crops through crop cutting experiments. 10
7. Discuss various steps involved in forecasting using ARMA model. 10
Define Infant Mortality Rate and its importance. Also describe various
methods of measuring corrected IMR. 15
State .the importance of population projection and outline component method (Frejka's) of population projection 15
8. Distinguish between Stable and Stationary population growth. Through stable population analysis, deduce that both birthrate and age distribution ij) are independent of time. 15
Explain Reed-Merrell method of constructing abridged life table and state its limitations. 10
Describe the multi collinearity problem in a generalized linear model. Outline Silvey's approach for tackling this problem. 15
1. Answer the following
Generate 10 randdm numbers from uniform using mixed congruential and multiplicative congruential methods.
Distinguish betwe..n Product control and Process control.
Show that the problem of two-person zero-sum game -can be viewed as a particular case of LPP.
illustrate one application each on MTTF and MTBF.
Describe CUSUM chart and write the procedure of constructing V-mask.
Maximize Z ax 2y subject to
-2x+3y S9
3x-2y S-20
Write the atgdrithm of solving a two-person zero-sum
max min mininax.
Explain the use ofiAOQL and LTPD as a measl,lre for constructing any sampling plan. 10.
Define the following:
Reliability function
Hazard functiod
Reliability of a leries system
Reliability of a ..arallel system
Use of bathtub model
3.(a)Explain the procedure of constructing control chart for fraction defectives and control chart for number of defectives. Also list out the applications for
A company has a demand of 1200 units/year for an item and it can produce 2000 such items per month. The cost of one setup is r 400 and the holding cost/unit/month is 15 paise. Find the following 10
Optimum lot size
Total inventory cost/year assuming the cost of 1 unit as r 4
Maximum inventory
new scooter costs r 6,000. The running cost and salvage (sale price) value at the end of the year are as under
Year 1 2 3 4 5 6 7
Running cost (in dallor)=1,200 1,400 1,600 1,800 2,000 2,400 3,000
Salvage value (in dallor) 4,000 2,666 2,000 1,500 1,000 600 600
If the interest rate is 10% per year and running costs are assumed to have occurred at midyear, find when the scooter should be replaced. 15
Draw a 5-point OC cuive for the single sampling plan
N 1000, n 150 and c 2 Also mention the merits and demerits of single and double sampling plans. 15
A shipping company has a single unloading dock with ships arriving in a Poisson fashion at an average rate of 3 per day. The unloading time distribution for a ship with n unloading crews is found to be exponential with average unloading time fri days. The company has a large labour supply without regular working hours and to avoid long waiting times, the company has a policy of using as many unloading crews as there are ships waiting in line or being unloaded. Find the following 10
Average number of unloading crews working at any time
Probability that 4 crews will be needed
Write on the following 15
Dam models
Transportation problem is a particular case of LPP
Statistical graphs using SPSS
SECTION-B
5. Answer the following::
Sx5=40
The average wage of a· labour worker for a day wast' 255 in 2000 and r 410 in 2014. If the consumer price indexes for these years were 155 and 240 respectively, find, the money wage increase in 2014 compared to 2000.
Define Net Reproduction Rate and Total Fertility Rate and explain their importance. in understanding the growth of a population.
(c)Mention and discpuss a test for homoscedasticity.
Define life table.I Explain various columns of abridged life table and their inter-relationshi s.
Explain the application of chi-square test in psychometry. In a study of 100 voters polled on an issue, sixty voted and forty voted Test the hypothesis that proportion-Pprop 0 · 70.
(Given, the critichl value of chi-square at, 0·5 level is 3·841)
6. Mention underlying assumption of multiple linear regression model. Derive the ordinary least sctuare estimator of the regression parameter in the multiple linear regression model. 15
What· are chain index numbers? How are they constructed?
In the constriU I ction of a certain cost of living index number, the following group index numbers were found. Calculate the cost of living index number by asing the weighted arithmetic mean and also by using the weighted gedmetric mean
proup IndexNumber Weight
Food 350 5
Fuel and lighting200 1
Clothing: 240 1
House: rent 160 1
Miscellancous 250 2
(c)Explain the sampling design and method of estimation for estimating yield estimation of major crops through crop cutting experiments. 10
7. Discuss various steps involved in forecasting using ARMA model. 10
Define Infant Mortality Rate and its importance. Also describe various
methods of measuring corrected IMR. 15
State .the importance of population projection and outline component method (Frejka's) of population projection 15
8. Distinguish between Stable and Stationary population growth. Through stable population analysis, deduce that both birthrate and age distribution ij) are independent of time. 15
Explain Reed-Merrell method of constructing abridged life table and state its limitations. 10
Describe the multi collinearity problem in a generalized linear model. Outline Silvey's approach for tackling this problem. 15