Exam Details
| Subject | statistics | |
| Paper | paper 4 | |
| Exam / Course | indian economic service and indian statistical service examination (ies/iss) | |
| Department | ||
| Organization | union public service commission | |
| Position | ||
| Exam Date | 2015 | |
| City, State | central government, |
Question Paper
Illustrate the Irreducible Markov chain with an example
Illustrate the Renewal process with an example
Illustrate the Wide-sense stationary process with an example
Illustrate the Martingale with an example
If is a Poisson process, then show that, as t 00
Pr
Mention the situation(s) where 'periodic review policy' and 'continuous review policy' in inventory theory are used, and elaborate the ideas of the above policies.
Prove that the number of basic V3Iiables in a balanced transportation problem is at most m n where m is the number of origins and n is the number of destinations.
Give all basic solutions to the foHo Ring
12x1 8x2 x3 80
x1 4x2 x4 48
Are these solutions feasible solutions for an LPP setup?
Define a Galton-Watson branching process. If {Pk is the offspring distribution, then prove the following identities P[Pn
Discuss a one-dimensional random walk.
What is Gambler's ruin problem? Obtain the probability of ruin, if Gambler plays with a capital of a rupees
What is a Wiener process? Obtain the forward diffusion equation of a Wiener process. Also discuss any two applications of this process.
Show that for M W 0 queue
model
Pn AoA1...An-1/M1M2...Mn Po
where An and Mn are the means of Poisson and exponential distributions respectively when there are n people in the system.
Solve the fcHowing problem by Simplex method:
Maximize Z 8x1 6x2
subject to x1 x2
2x1 3x2 25
x1 5x2 35
x1, X2 0
A solicitors' firm employs typists on hourly price-rate basis for their daily work. There are five typists and thEir charges and speeds are different. According to an earlier understanding, only one job is given to one typist and the typist is paid for a full hour even if he works for a fraction of an hour. Find the least cost allocation for the following data
typist Rare per hour No. of pages typed/hour
A 5 12
B 6 14
C 3 8
D 4 10
E 4 11
Job No.of pages
P 199
Q 175
R 145
S 298
T 178
Derive a formula to simulate a random observation from a Poisson random variable.
What is the basis of classification of inventory in ABC analysis.? Illustrate with a simple example.
Define a Poisson process. Stating the regularity conditions, show that is given by the Poisson law
Pn(t) n ..,
If Xn is a branching process with
E(X1) m EkPk to 00)
and 02 var then show that
(i) m^n
(ii) var{Xn}
Trim Sheet Company reqUIres rectangular sheets of width 7 311d 9 inches to be cut from a roll of width 20 inches. One-dimensional cutting is considered. The requirements are 300, 400 and 600 sheets of the three widths respectively. Write a linear programming problem to minimize waste assuming that the excess sheet:; cut are treated as waste.
Given the following basic feasible solution to a transportation problem, obtain four iterations of the optimal solution using stepping stone method :
<img src='./qimages/16050-4d.jpg'>
Explain stationary and stable population. State the situation when the age distribution of two stable populations would be identical.
Compute the crude and standardized death rates of the populations A and regarding A as standard population, from the following data :
Age group (years) A B
Population Deaths Population Deaths
Under 10 20000 600 12000 372
10-20 12000 240 30000 660
20-40 50000 1250 62000 1602
40-60 30000 1050 15000 523
Above 60 10000 500 3000 180
Explain briefly the uses of life table.
Explain stack and queue structures with suitable examples. Write the algorithm to and 'delete' into a stack and queue covering all possible cases.
Write an algorithm/flowchart for computing product of two matrices A and B of orders m x n and n x p respectively.
Discuss the main sources of demographic data in the Indian system. Give your suggestion for the measures to improve the quality of data.
Compute GFR, SFR, TFR and GRR from the data given below
Age group of child bearing females 15-19 20-24 25-29 30-34
Number of women 16·0 16.4 15.8 15·2
Age group of child bearing females 35-39 40-44 45-49
Number of women 14·8 15·0 14·5
Assume that the proportion of female births is 46·2 percent.
Describe King's method for constructing an abridged life table.
Explain the Matrix method of population projection.
A list of n distinct integers is given. Write an algorithm/flowchart, using minimum number of comparison operations, to find out the second maximum number (i.e., the number less than the maximum number but greater than the others).
Describe various types of keys, with appropriate examples, in regard to a database management system.
Write down the algorithm to evaluate
Integral dx(limits a to b)
using Weddle's rule. How do you implement it in finding P(x where Write an algorithm/flowchart to check whether an input non-zero integer n is prime. Prove that the main loop of the algorithm/flowchart for this purpose is to be executed up to times, where stands for the least integer greater than or equal to Explain the meaning of Crude death rate in vital statistics and discuss their importance.Briefly indicate how these rates can be used in population projection.
Explain the meaning of Standard birthrate in vital statistics and discuss their importance. Briefly indicate how these rates can be used in population projection.
Explain the meaning of General fertility rate in vital statistics and discuss their importance. Briefly indicate how these rates can be used in population projection.
Describe the procedure and steps for the construction of life table.
Describe various types of operating
systems.
Consider the following four numbers
a =567 in octal representation
b ABC in hexadecimal representation
c 220 ill a hypothetical number
system with base 3
d 786 In another hypothetical number system with base 9
Answer the following questions Convert a directly into the corresponding number in hexadecimal representation.
(ii) Convert c directly into the corresponding number in the hypothetical number system with base 9.
(iii) Add a and b to produce the results in hexadecimal number system.
Add c and d to generate the result in the hypothetical number system with base 9.
Illustrate the Renewal process with an example
Illustrate the Wide-sense stationary process with an example
Illustrate the Martingale with an example
If is a Poisson process, then show that, as t 00
Pr
Mention the situation(s) where 'periodic review policy' and 'continuous review policy' in inventory theory are used, and elaborate the ideas of the above policies.
Prove that the number of basic V3Iiables in a balanced transportation problem is at most m n where m is the number of origins and n is the number of destinations.
Give all basic solutions to the foHo Ring
12x1 8x2 x3 80
x1 4x2 x4 48
Are these solutions feasible solutions for an LPP setup?
Define a Galton-Watson branching process. If {Pk is the offspring distribution, then prove the following identities P[Pn
Discuss a one-dimensional random walk.
What is Gambler's ruin problem? Obtain the probability of ruin, if Gambler plays with a capital of a rupees
What is a Wiener process? Obtain the forward diffusion equation of a Wiener process. Also discuss any two applications of this process.
Show that for M W 0 queue
model
Pn AoA1...An-1/M1M2...Mn Po
where An and Mn are the means of Poisson and exponential distributions respectively when there are n people in the system.
Solve the fcHowing problem by Simplex method:
Maximize Z 8x1 6x2
subject to x1 x2
2x1 3x2 25
x1 5x2 35
x1, X2 0
A solicitors' firm employs typists on hourly price-rate basis for their daily work. There are five typists and thEir charges and speeds are different. According to an earlier understanding, only one job is given to one typist and the typist is paid for a full hour even if he works for a fraction of an hour. Find the least cost allocation for the following data
typist Rare per hour No. of pages typed/hour
A 5 12
B 6 14
C 3 8
D 4 10
E 4 11
Job No.of pages
P 199
Q 175
R 145
S 298
T 178
Derive a formula to simulate a random observation from a Poisson random variable.
What is the basis of classification of inventory in ABC analysis.? Illustrate with a simple example.
Define a Poisson process. Stating the regularity conditions, show that is given by the Poisson law
Pn(t) n ..,
If Xn is a branching process with
E(X1) m EkPk to 00)
and 02 var then show that
(i) m^n
(ii) var{Xn}
Trim Sheet Company reqUIres rectangular sheets of width 7 311d 9 inches to be cut from a roll of width 20 inches. One-dimensional cutting is considered. The requirements are 300, 400 and 600 sheets of the three widths respectively. Write a linear programming problem to minimize waste assuming that the excess sheet:; cut are treated as waste.
Given the following basic feasible solution to a transportation problem, obtain four iterations of the optimal solution using stepping stone method :
<img src='./qimages/16050-4d.jpg'>
Explain stationary and stable population. State the situation when the age distribution of two stable populations would be identical.
Compute the crude and standardized death rates of the populations A and regarding A as standard population, from the following data :
Age group (years) A B
Population Deaths Population Deaths
Under 10 20000 600 12000 372
10-20 12000 240 30000 660
20-40 50000 1250 62000 1602
40-60 30000 1050 15000 523
Above 60 10000 500 3000 180
Explain briefly the uses of life table.
Explain stack and queue structures with suitable examples. Write the algorithm to and 'delete' into a stack and queue covering all possible cases.
Write an algorithm/flowchart for computing product of two matrices A and B of orders m x n and n x p respectively.
Discuss the main sources of demographic data in the Indian system. Give your suggestion for the measures to improve the quality of data.
Compute GFR, SFR, TFR and GRR from the data given below
Age group of child bearing females 15-19 20-24 25-29 30-34
Number of women 16·0 16.4 15.8 15·2
Age group of child bearing females 35-39 40-44 45-49
Number of women 14·8 15·0 14·5
Assume that the proportion of female births is 46·2 percent.
Describe King's method for constructing an abridged life table.
Explain the Matrix method of population projection.
A list of n distinct integers is given. Write an algorithm/flowchart, using minimum number of comparison operations, to find out the second maximum number (i.e., the number less than the maximum number but greater than the others).
Describe various types of keys, with appropriate examples, in regard to a database management system.
Write down the algorithm to evaluate
Integral dx(limits a to b)
using Weddle's rule. How do you implement it in finding P(x where Write an algorithm/flowchart to check whether an input non-zero integer n is prime. Prove that the main loop of the algorithm/flowchart for this purpose is to be executed up to times, where stands for the least integer greater than or equal to Explain the meaning of Crude death rate in vital statistics and discuss their importance.Briefly indicate how these rates can be used in population projection.
Explain the meaning of Standard birthrate in vital statistics and discuss their importance. Briefly indicate how these rates can be used in population projection.
Explain the meaning of General fertility rate in vital statistics and discuss their importance. Briefly indicate how these rates can be used in population projection.
Describe the procedure and steps for the construction of life table.
Describe various types of operating
systems.
Consider the following four numbers
a =567 in octal representation
b ABC in hexadecimal representation
c 220 ill a hypothetical number
system with base 3
d 786 In another hypothetical number system with base 9
Answer the following questions Convert a directly into the corresponding number in hexadecimal representation.
(ii) Convert c directly into the corresponding number in the hypothetical number system with base 9.
(iii) Add a and b to produce the results in hexadecimal number system.
Add c and d to generate the result in the hypothetical number system with base 9.