Indian Statistical Service Exam, Statistics IV Exam paper

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SECTION A
1. (a) For an periodic, positive persistent state j, show
that lim p(!" = 1 / pj , where p. dcnotes the " JJ J
mean recurrence time of state j. 8

(b) For a Poisson process I X(t), t 2 0 I , show that
the condit~onal distribution of X(s) given X(t),
0 < s < t is binomial. 8

(c) Describe the pure birth process. Derive an
exprcssion for Po,iO, t) = PIXit) = n 1 X(0) = 01 [or
the Yule -Furry process. 8

(d) Definc (il lead time (ii) buffer stock in an
inventory problem. How do you determine the
buffer stock in an EOQ situation ? 6

(e) Explain the 'Gap test' and the 'Poker test' fbr
testing randomness of observations fi.om uniform
distribution. 8

2. (a) Let It,,, n > 1) be a sequence of i.i.d.r.v.'s w~th
P(tk = 1) = p and P(tk = 0) = 4, P + 4 = 1
Define Y,, = n - ti, n = 1, 2,

Show that IY,, n > 11 is a Markov chain. Obtain
its one-step transition probability matrix. 10
C-JTT-M-TUD 2 LContd.1

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Hello sir I am Harsh, please provide me the previous year exam paper of Indian Statistical Service Exam, Statistics IV??

Here as per your demand I am providing you exam paper of Indian Statistical Service Exam, Statistics IV of 2015

Exam paper of Indian Statistical Service Exam, Statistics IV of 2015








ISS Syllabus: Statistics-IV
Stochastic Processes
Specifications of a Stochastic Process, Markov chains, dassification of states, limiting probabilities; stationary distribution; Random walk and Gambler's ruin problem. Poisson process, Birth and death process; applications to Queues-M/M/ 1 and M/WC models. Branching Process.

Operations Research

Elements of linear programming. Simplex procedure. Principle of duality. Transport and assignment problems. Single and multi-period inventory control models. ABC analysis. General simulation problems. Replacement models for items that fail and or items that deteriorate.

Demography and Vital Statistics
The life table, its constitution and properties. Makehams and Gompertz curves. National life tables. UN model life tables. Abridged life tables. Stable and stationary populations. Different birth rates. Total fertility rate. Gross and net reproduction rates. Different mortality rates. Standardised death rate. Internal and international migration: Net migration. International and postcensal estimates. Projection method including logistic curve fitting. Decennial population census in India.

Computer Application and Data Processing
Computer Application
Computer system concepts: Computer system components and functions. The Central Processing unit, Main memory, Bit, Byte, Word, Input/Output Devices, Speeds and memory Capacities in computer systems. Software concepts: Overview of Operating Systems, Types and Functions of Operating System, application Software, Software for multi-tasking, multi-programming, Batch Processing Mode, Time sharing mode, Concept of System Support Program, Overview of Existing Software packages on Word Processing and Spreadsheets. Overview of an application Specific Program: Flow charts, Basics of Algorithm, Fundamental of design and analysis of Algorithm: Basics of data Structure, Queue, Stack.

Data Processing

Data processing: Digital Number System, Number conversions, Binary representation of integers, Binary representation of real numbers, Logical Data element like character, fields, records, files, Fundamentals of data transmission and processing including error control and error processing. Data base management: Data Resource management. Data base and file organization and processing. Direct, Sequential, Indexed Sequential file. Concepts of Client Server architecture, Data Base Administrator. An overview of DBMS software.

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