Vinayaka Mission University
Vinayaka Missions University (VMU) is a pioneering and vibrant school offering a multi-social experience with an atmosphere checked by the ideal congruity of living in differing qualities.
Years1
UNIT - 01
RANDOM VARIABLE AND DISTRIBUTION FUNCTION - BASIC DISTRIBUTION THEORY -
RANDOM VARIABLES - DISTRIBUTION FUNCTION - PROPERTIES - JOINT - PROBABILITY
MASS FUNCTION - JOINT PROBABILITY DISTRIBUTION FUNCTION - MARGINAL
DISTRIBUTION FUNCTION - JOINT DENSITY FUNCTION - CONDITIONAL DISTRIBUTION
FUNCTION.
UNIT - 02
FUNCTIONS OF RANDOM VARIABLES - TRANSFORMATION TECHNIQUES - DISTRIBUTION
FUNCTION TECHNIQUE - TRANSFORMATION TECHNIQUE - MOMENT GENERATING
FUNCTION TECHNIQUE - FUNCTIONS OF TWO DIMENSIONAL INDEPENDENT RANDOM
VARIABLE.
UNIT - 03
DISTRIBUTION OF SUM OF RANDOM VARIABLES - DISTRIBUTION OF PRODUCT OF
RANDOM VARIABLES - DISTRIBUTION OF QUOTIENT OF RANDOM VARIABLE -
MULTIVARIATE NORMAL DISTRIBUTION - BI VARIATE NORMAL DISTRIBUTION - MGF OF
BIVARIATE.
UNIT - 04
NORMAL DISTRIBUTION - MULTI VARIATE NORMAL DISTRIBUTION - PROPERTIES -
MARGINAL AND CONDITIONAL DISTRIBUTION - MULTINOMIAL DISTRIBUTION -
PROPERTIES - CHAPTER NON- CONTROL PROBABILITY DISTRIBUTION - NON - CENTRAL -
CHI - SQUARE DISTRIBUTION - CHARACTER FUNCTION - ADDICTIVE PROPERTY -
MOMENTS - NON-CENTRAL T - DISTRIBUTION - NON-CENTRAL F- DISTRIBUTION - MEAN
AND VARIABLE.
UNIT - 05
DISTRIBUTIONS - A QUADRATIC FORMS - DISTRIBUTION OF QUADRATE FORM UNDER
NORMALITY - NECESSARY AND SUFFICIENT CONDITION FOR THE QUADRATIC
FUNCTION TO HAVE A DISTRIBUTION - INDEPENDENCE OF TWO QUADRATE FUNCTION.
UNIT - 06
COCHRAN`S THEOREM - COMPOUND - TRUNCATED AND MIXTURE DISTRIBUTION
(STANDARD CASE ONLY).
UNIT - 07
COMPOUND DISTRIBUTION AND TRUNCATED DISTRIBUTION - COMPOUND
DISTRIBUTION.
UNIT - 08
BINOMIAL DISTRIBUTION - POISSON`S DISTRIBUTIONS - TRUNCATED DISTRIBUTION -
GEOMETRIC DISTRIBUTION.
UNIT - 09
NORMAL DISTRIBUTION - STANDARD CAUCHY DISTRIBUTION - STANDARD NORMAL
Vinayaka Missions University,Directorate of Distance Education
Salem India
MASTER OF SCIENCE IN STATISTICS
1 Yr.
DISTRIBUTION THEORY AND PRACTICAL(2030605)
UNIT - 10
CORRELATION AND REGRESSION - SIMPLE CORRELATION - PARTIAL CORRELATION -
MULTIPLE CORRELATION.
UNIT - 11
SIMPLE REGRESSION (CONCEPTS AND SIMPLE PROBLEM ONLY).
UNIT - 12
DISTRIBUTION OF ORDER STATISTICS - ORDER STATISTICS - THEIR DISTRIBUTION AND
PROPERTIES - JOINT AND MARGINAL DISTRIBUTION OF ORDER STATISTICS - EXTREME
VALUES AND THEIR ASYMPTOTIC DISTRIBUTION (STATEMENT ONLY WITH
APPLICATIONS).
BASIC CONCEPTS - FIELDS - MEASURE - ALGEBRA OF SETS - COUNTABLE SETS - FIELD -
MONATOMIC FIELD - MONATOMIC CLASS - MINIMAL CLASS - MINIMAL - FIELD -
GENERATED BY THE CLASS OF SET
BOREAL SET - BOREL FIELD - BOREL - FIELD - SET FUNCTIONS - FINITELY ADDITIVE SET
FUNCTION - COUNTABLE ADDITIVE SET FUNCTIONS
MEASURE - SINGULAR MEASURE - COUNTING MEASURE - LEBESQUE MEASURE -
LEBESQUE - SATIETIES MEASURE - BASIC CONCEPTS FIELD - MONATOMIC FIELD -
MINIMAL - FIELD
BOREAL SET - COUNTABLE SET ADDITIVE SET FUNCTIONS - ADDITIVE SET FUNCTIONS -
MEASURE FUNCTIONS
INTRODUCTION - MEASURE FUNCTION - ITS PROPER - BOREAL CATELLI LEMMA -
MEASURABLE SETS - EXTENSION MEASURE - LEBESQUE MEASURE - LEBESQUE
SATIETIES - MEASURABLE FUNCTION
APPROXIMATION THEOREM - MEASURE INTEGRATION AND CONVERGENCE OF
MEASURE
INTRODUCTION - MEASURE INTEGRATION - LEBESQUE DOMINATED CONVERGENCE
THEOREM - MODE OF CONVERGENCE - MONOTONIC CONVERGENCE THEOREM -
PRODUCT MEASURE FUNCTION
INTRODUCTION - PRODUCT MEASURE FUNCTION - PRODUCT MEASURE THEOREM -
FUBINI THEOREM
RANDON - NIBODYM THEOREM - PROBABILITY MEASURE AND RANDOM VARIABLE
INTRODUCTION - PROBABILITY MEASURE AND ITS PROPERTIES - DISCRETE
PROBABILITY - SPACE GENERAL PROBABILITY SPACE - CONTINUOUS PROBABILITY
SPACE - FUNCTIONS AND INVERSE FUNCTIONS - RANDOM VARIABLE - INDUCED
PROBABILITY SPACE BY THE RANDOM VARIABLE - DISTRIBUTION FUNCTION - JORDON
DECOMPOSITION THEOREM - INDEPENDENCE - EXPECTATION - MODES OF
CONVERGENCE
MEASUREMENT AND PROBABILITY THEORY(2030606)
INTRODUCTION - CONCEPT OF INDEPENDENCE - KOLMOGOROR - 0 -1 -HAS & BOREL
LEMMA
EXPECTATION OF A RANDOM VARIABLE - MOMENTS - INEQUALITIES - CONVERGENCE
OF SEQUENCE OF RANDOM VARIABLES - CHARACTERISTIC FUNCTION - LAW OF LARGE
NUMBERS
INTRODUCTION - CHARACTERISTIC FUNCTION - INVERSION THEOREM - LEVY
CONTINUITY THEOREM - UNIQUENESS THEOREM - LAW OF LARGE NUMBERS - WEAK
AND COMPLETE CONVERGENCE OF DISTRIBUTION FUNCTION CENTRAL LIMIT THEOREM
INTRODUCTION - WEAK AND COMPLETE CONVERGENCE OF DISTRIBUTION FUNCTION -
HELLY - BRAY THEOREM - CENTRAL LIMIT THEOREMS.
INTRODUCTION TO REAL NUMBERS - SETS - FIELD STRUCTURE AND ORDER
STRUCTURE - INTERVALS - OPEN AND CLOSED - BOUNDED AND UNBOUNDED SETS.
ABSOLUTE VALUES (MODULUS) OF A REAL NUMBERS - N - DIMENSIONAL EUCLIDIAN
SPACE.
COMPACT SETS - METRIC SPACES - COMPACT SUBSETS OF METRIC SPACES - BOLZANO
- WEIRSTRESS THEOREM - HEINE - BOND THEOREM.
SEQUENCES - BOUNDS OF A SEQUENCE - CONVERGENCE OF SEQUENCE - LIMIT POINT
OF SEQUENCE - CAUCLY SEQUENCE - MONOTONIC SEQUENCES - SERIES.
CONVERGENCE FOR SERIES - UNIFORM CONVERGENCE AND ITS APPLICATION
(WITHOUT PROOF).
REAL VALUED FUNCTION OF SEVERAL VARIABLES - LIMIT - CONTINUITY AND
DERIVABILITY OF FUNCTION.
CHARACTRISTICS ROOTS AND VECTORS - CAYLEY - HAMMILTON THEOREM - MINIMAL
POLYNOMIAL - SIMILAR MATRICES.
ALGEBRAIC AND GEOMETRIC MULTIPLICITY OF CHARACTERISTIC ROOTS.
SYMMETRIC MATRIX - SPECTRAL DECOMPOSITION OF A REAL SYMMETRIC MATRIX -
REDUCTION OF PAIR OF REAL SYMMETRIC MATRICES - HERMITION MATRICES.
REAL QUADRATIC FORMS - REDUCTION AND CLASSIFICATION OF QUADRATIC FORMS.
EXTREMA OF QUADRATIC FORMS - INDEX AND SIGNATURE - TRIANGULAR REDUCTION
OF A POSITIVE DEFINITE MATRIX.
GENERALIZED INVERSE OF A MATRIX - MOORE AND PENROSE GENERALIZED INVERSE
IN THE SOLUTION OF SYSTEM OF LINEAR EQUATIONS - LEAST SQUARE PROPERTIES OF
MORE AND PENROSE GENERALIZED INVERSE - APPLICATION OF M-P INVERSE FOR THE
SOLUTION OF OPTIMIZATION PROBLEMS.
INTRODUCTION TO SAMPLE SURVEYS - POPULATION AND SAMPLE - CENSUS AND
SAMPLE SURVEYS - REQUIREMENTS OF A GOOD SAMPLE - PRINCIPLES OF SAMPLING -
ADVANTAGES AND LIMITATIONS OF SAMPLING.
TYPES OF SAMPLING - CENSUS OF BINS - PRINCIPAL STEPS INVOLVED IN SAMPLE
SURVEY - SAMPLING DISTRIBUTION AND STANDARD ERROR.
ORGANIZATIONS AND ERRORS IN PREPARATION OF QUESTIONNAIRE AND SCHEDULE -
PILOT SURVEY - CENTRAL STATISTICAL ORGANIZATION (CSO).
NATIONAL SAMPLE SURVEY ORGANIZATION (NSSO) - SAMPLING AND NON-SAMPLING
ERROR - RESPONSE AND NON-RESPONSE ERROR - TYPES OF NON-RESPONSE -
INTERPENETRATING SUB SAMPLES.
SIMPLE RANDOM AND STRATIFIED - SIMPLE RANDOM SAMPLING WITH AND WITH OUT
REPLACEMENT - NOTATION - UNBIASED ESTIMATE OF MEAN - VARIANCE OF ESTIMATED
MEAN.
STRATIFIED RANDOM SAMPLING - NOTATIONS - UNBIASED ESTIMATE OF MEAN -
VARIANCE OF ESTIMATED MEAN - CONCEPT OF STRATIFYING FACTOR - PROBLEMS -
PROPORTIONAL ALLOCATION - OPTIMUM ALLOCATION.
COST FUNCTION - COMPARISON OF SIMPLE RANDOM SAMPLING - STRATIFIED RANDOM
SAMPLING WITH PROPORTIONAL - OPTIMUM ALLOCATION.
SYSTEMATIC SAMPLING - LINEAR SYSTEMATIC SAMPLING - CIRCULAR SYSTEMATIC
SAMPLING - NOTATIONS - UNBIASED OF ESTIMATED MEAN - VARIANCE OF ESTIMATED
MEAN - COMPARISON OF SYSTEMATIC SAMPLING AND SIMPLE RANDOM SAMPLING -
WITHOUT REPLACEMENT (SRSWOR) - VARIANCE OF ESTIMATED MEAN IN TERMS OF
INTRA-CLASS CORRELATION - COEFFICIENT - RELATIVE EFFICIENCY OF SYSTEMATIC
SAMPLING OVER SRSWOR - SYSTEMATIC SAMPLING VIEWED AS STRATIFIED SAMPLING.
VARIANCE OF MEAN IN TERMS OF STRATUM - RELATIVE EFFICIENCY OF SYSTEMATIC
SAMPLING OVER STRATIFIED SAMPLING - COMPARISON OF SIMPLE, SYSTEMATIC AND
STRATIFIED SAMPLING - CLUSTER SAMPLING - NEED FOR CLUSTER SAMPLING -
ADVANTAGES AND DISADVANTAGES - FORMATION OF CLUSTER - COMPARISON OF
CLUSTER SAMPLING WITH STRATIFIED SAMPLING.
SAMPLING THEORY[MSC-STAT](2030610)
NOTATIONS - VARIANCE OF ESTIMATED MEAN IN TERMS OF INTRA- CLUSTER
CORRELATION COEFFICIENT - SYSTEMATIC SAMPLING VIEWED AS CLUSTER SAMPLING
- COST FUNCTION - DETERMINATION OF OPTIMUM CLUSTER SIZE - PROBABILITY
PROPORTIONAL TO SIZE (PPS) SAMPLING - LAHIRI`S METHOD - PPS SAMPLING WITH
REPLACEMENT (PPSWR) - PPS SAMPLING WITHOUT REPLACEMENT (PPSWOR) -
HURWITZ- THOMPSON ESTIMATOR - YATE`S AND GRUNDY FORM - CUMULATIVE TOTAL
METHOD.
RATIO AND REGRESSION ESTIMATORS - DOUBLE SAMPLING - DOUBLE SAMPLING FOR
RATIO ESTIMATOR - DOUBLE SAMPLING FOR RATIO ESTIMATOR - OPTIMUM
ALLOCATION - REGRESSION ESTIMATOR FOR DOUBLE SAMPLING - COMPARISON OF
OPTIMUM ALLOCATION - MULTI-STAGE SAMPLING - MULTI-PHASE SAMPLING.
ROLE OF SAMPLE SURVEYS IN NATIONAL - RANDOMIZED RESPONSE TECHNIQUE -
WARNER`S METHOD - UNRELATED QUESTION METHOD - POPULATION PROJECTIONS
USING LESLIE MATRIX - PROPERTIES OF LESLIE MATRIX - SAMPLE SURVEYS FOR
NATIONAL DEVELOPMENT - POPULATION GROWTH IN DEVELOPMENT COUNTRIES -
HUMAN DEVELOPMENT INDEX - NATIONAL INCOME - MEASURING INEQUALITY INCOMES.
BASIC CONCEPTS OF OOPS AND C++ - OBJECT ORIENTED PROGRAMMING STRUCTURE
- DEFINITION AND FEATURES - OOPS CONCEPTS - PRINCIPLES OF OOPS.
APPLICATION OF OOPS - BEGINNING WITH C++ - APPLICATIONS OF C++ - STRUCTURE
OF C++ PROGRAM - BASIC PROGRAM CONSTRUCTION - COMPUTING AND LINKING.
DATA TYPE - TOKENS - KEYWORDS - IDENTIFIERS - DATA TYPE - OPERATORS -
MANIPULATORS - EXPRESSIONS AND THEIR TYPES - LIBRARY FUNCTIONS - IMPLICIT
CONVERSION - OPERATOR OVERLOADING - OPERATOR PRECEDENCE.
CONTROL STRUCTURES - DECISIONS - LOGICAL OPERATORS - CONTROL STATEMENTS.
FUNCTION - FUNCTIONS MAIN FUNCTION - SIMPLE FUNCTION - PASSING ARGUMENTS
TO FUNCTIONS - RETURNING VALUES FROM FUNCTION - REFERENCE ARGUMENTS -
OVERLOADED FUNCTIONS - INLINE FUNCTIONS - DEFAULT ARGUMENTS.
VARIABLE AND STORAGE CLASSES - FRIEND AND VIRTUAL FUNCTIONS - MEMBER
FUNCTIONS - NESTING OF FUNCTION - PRIVATE FUNCTIONS - STATIC FUNCTIONS.
OBJECTS POINTERS CONSTRUCTORS - OBJECTS - MEMORY ALLOCATION OF OBJECTS -
ARRAY OF OBJECTS - OBJECT AS FUNCTION ARGUMENTS - FRIENDLY FUNCTIONS -
RETURNING OBJECTS - POINTER TO MEMBERS.
CONSTRUCTOR - PARAMETERIZED CONSTRUCTORS - MULTIPLE CONSTRUCTOR - COPY
- DYNAMIC CONSTRUCTOR - CONSTRUCTING TWO DIMENSIONAL ARRAYS -
CONSTRUCTOR WITH DEFAULT ARGUMENTS.
DESTRUCTORS - DESTRUCTORS - OPERATOR OVERLOADING - OPERATOR
OVERLOADING TYPE - RULES FOR OPERATOR OVERLOADING - DATA CONVERSION -
BETWEEN BASIC TYPES - BETWEEN OBJECTS AND BASIC TYPE - BETWEEN OBJECTS OF
DIFFERENT CLASS - DRAWBACKS OF OVERLOADING AND CONVERSION.
INHERITANCE - INHERITANCE - DEFINING DERIVED CLASS - SINGLE - MULTIPLE -
MULTILEVEL INHERITANCE - HIERARCHICAL - HYBRID INHERITANCE - INHERITING
PRIVATE MEMBERS - VIRTUAL BASE CLASS - ABSTRACT CLASS - MEMBER CLASSES -
NESTING OF CLASSES - POINTER - POINTER TO OBJECTS & DERIVED CLASSES - THIS
POINTER - VIRTUAL AND PURE VIRTUAL FUNCTIONS.
STATISTICAL COMPUTING C++(2050147)
CONSOLE INPUT / OUTPUT OPERATIONS - POLYMORPHISM - CONSOLE I/O OPERATIONS
- BASIC CONCEPT OF INPUT / OUTPUT FILES - EXCEPTION HANDLING - HANDLING
MECHANISM - THROWING & CATCHING APPLICATIONS - MATRIX OPERATIONS -
ARRANGE THE OBSERVATION IN INCREASING / DECREASING ORDER OF COMPUTATION
OF MEAN - MEDIAN VARIANCE - CO-EFFICIENT OF VARIATION (DISCRETE CASE ONLY).
STATISTICAL ANALYSIS - ANOVA - ONE WAY - TWO WAY CLASSIFICATION - T-TEST
BASED ON MEAN - DIFFERENCE OF MEANS - F TEST FOR THE EQUALITY OF VARIANCE -
CHI -SQUARE TEST FOR INDEPENDENCE OF ATTRIBUTES - GOODNESS OF FIT
(BINOMIAL, POISSON ONLY).
CRITERIA OF POINT ESTIMATION - POINT ESTIMATOR - CONSISTENCY - UNBIASED NESS.
SUFFICIENCY - EFFICIENCY - JOINT SUFFICIENCY.
OPTIMAL ESTIMATION - UMVU - UNCORRELATED APPROACH - RAO - BLACKWELL
THEOREM - LEHMAN.
SCHEFFE THEOREM - C.R - INEQUALITY - CHAPMAN - ROBINS IN EQUALING -
BHATTACHARYA INEQUALITY.
METHODS OF ESTIMATION - METHOD OF MLE - MINIMUM VARIANCE BOUND ESTIMATION
- MOMENT ESTIMATION.
METHOD OF LEAST SQUARE - GAURS MARK OF THEOREM.
INTERNAL ESTIMATION - INTRODUCTION - CONFIDENCE INTERVALS.
ALTERNATIVE METHOD OF CONFIDENCE INTERNALS - SHORTEST LENGTH CONFIDENCE
INTERNALS.
BAYES ESTIMATION - BAYES POINT ESTIMATION.
BAYES CONFIDENCE INTERNALS.
THEORY OF ESTIMATION(2030612)
Years2
DISTRIBUTION FUNCTION OF TWO DIMENSIONAL RANDOM VARIABLE PROPERTIES.
DISTRIBUTION OF SUM - DIFFERENCE PRODUCT AND QUOTIENT OF TWO INDEPENDENT
RANDOM VARIABLES.
ELEMENTARY IDEAS ON LOGARITHMIC SERIES DISTRIBUTION - NON-CENTRAL CHISQUARE.
T AND F DISTRIBUTIONS - DISTRIBUTION OF ORDER STATISTICS - DISTRIBUTION OF
RANGE AND MEDIAN.
LIMITING DISTRIBUTION OF EXTREME ORDER STATISTICS.
BIVARIATE AND MULTIVARIATE NORMAL DISTRIBUTION - PROPERTIES.
MARGINAL AND CONDITIONAL DISTRIBUTIONS.
DISTRIBUTION OF QUADRATIC FORMS IN NORMAL VARIABLES.
NECESSARY AND SUFFICIENT CONDITION FOR A QUADRATIC FORM TO BE DISTRIBUTED
AS CHI - SQUARE DISTRIBUTION.
COCHRAN`S THEOREM - JAMES THEOREM.
MAXIMUM LIKELIHOOD ESTIMATE OF PARAMETERS OF MULTIVARIATE NORMAL
DISTRIBUTIONS OF SAMPLE MEAN VECTOR - INFERENCE ABOUT MEAN VECTOR OF ONE
AND TWO MULTIVARIATE NORMAL POPULATION.
2 Yr.
DISTRIBUTION THEORY(2030615)
THEORY OF GAMES - INTRODUCTION - PURE STRATEGIES - MIXED STRATEGIES - RULES
OF DOMINANCE - GAMES WITHOUT SADDLE POINT - ALGEBRIC METHOD. ARITHMETIC
GAMES - MATRIX METHOD - GRAPHICAL METHODS - LINEAR PROGRAMMING METHOD.
O.R. - J.K. SHARMA - SECTION 11.1 TO 11.6.
INVENTORY CONTROL - MEANING - CLASSIFICATION - ADVANTAGES -
CHARACTERISTICS - INVENTORY MODEL BUILDING - DETERMINISTIC INVENTORY
MODEL WITH NO SHORTAGE - MODEL
I - I (A), I(B), I (C) - WITH SHORTAGE - MODEL - 2(A) , 2(B), 2(C) - MULTI ITEM INVENTORY
MODEL - MODEL - 3(A), 3(B)- PROBABILISTIC INVENTORY CONTROL - STATIONARY
DEMAND MODELS - MODEL 1(A), MODEL 2(A) , MODEL 3 (A).
O.R. - J.K. SHARMA - SECTION 13.1 TO 13.9.
O.R. - TAHA - SECTION 16.3, 16.3.1. 16.3.2.
QUEUING THEORY :
INTRODUCTION - FEATURES - CHARACTERISTICS - CLASSIFICATION - SOLUTION OF
QUEUING MODELS - (M/M/1) : (O/FCFS) (Q/S/RO) (M/M/1) : (N/FCFS) (M/M/S) : (N/FCFS) -
(M/EK/1) : (O/FCCS) - (M/G/1) AND (G1/M/1).
O.R. - J.K. SHARMA - SECTION 15.1 TO 15.6
STOCHASTIC PROCESS - J. MEDHI - SECTION 10.6.
REPLACEMENT MODEL :
INTRODUCTION - FAILURE - GRADUAL FAILURE, SUDDEN FAILURE - REPLACEMENT OF
ITEMS DETERIORATE WITH TIME - REPLACEMENT OF ITEMS WHOSE MAINTENANCE
COST INCREASE WITH TIME - SELECTION OF BEST ITEM AMONGST TWO -
REPLACEMENT OF ITEMS THAT FIL COMPLETELY - GROUP REPLACEMENT. O.R. - J.K.
SHARMA - SECTION 16.1 TO 16.4.
SIMULATION :
INTRODUCTION - MONTE CARLO SIMULATION - TYPES OF SIMULATION - STEPS IN
SIMULATION - ADVANTAGES - DISCRETE EVEN SIMULATIONS - GENERALIZATION OF
RANDOM NUMBERS - MECHANICS OF DISCRETE SIMULATION. O.R. - J.K. SHARMA -
SECTION 18.1 TO 18.8.
O.R. TAHA - SECTION 18.1 TO 18.6.
OPERATIONS RESEARCH(MSC-STAT)(2030616)
FIELDS - VECTOR SPACES - SUBSPACES - LINEAR DEPENDENCE AND INDEPENDENCE -
BASIS AND DIMENSION OF A VECTOR SPACE - FINITE DIMENSIONAL VECTOR SPACES.
COMPLETION THEOREM - EXAMPLES OF VECTOR OVER REAL AND COMPLEX FIELDS -
LINEAR EQUATIONS - VECTOR SPACES WITH AN INNER PRODUCT, GRAM-SCHMIDT
ORTHOGONALIZATION PROCESS.
ORHTONORMAL BASIS AND ORTHOGONAL PROJECTION OF A VECTOR - LINEAR
TRANSFORMATIONS - K ALGEBRA OF MATRICES - ROW AND COLUMN SPACES OF A
MATRIX.
ELEMENTARY MATRICES - DETERMINANTS - RANK AND INVERSE OF A MATRIX - NULL
SPACES AND NULLITY - PARTITIONED MATRICES - KRONECKER PRODUCT.
HERMIT CANONICAL FORM - GENERALIZED INVERSE - MOORE - PENROSE GENERALIZED
INVERSE - IDEMPOTENT MATRICES - SOLUTIONS OF MATRIX EQUATIONS.
REAL QUADRATIC FORMS - REDUCTION AND CLASSIFICATION OF QUADRATIC FORMS -
INDEX AND SIGNATURE - TRIANGULAR REDUCTION OF A POSITIVE DEFINITE MATRIX.
CHARACTERISTIC ROOTS AND VECTORS - CAYLEY - HAMITION THEOREM - MINIMAL
ALGEBRAIC AND GEOMETRIC MULTIPLICITY OF A CHARACTERISTIC ROOT.
SPECTRAL DECOMPOSITION OF A REAL SYMMETRIC METRIC - REDUCTION OF A PAIR
OF REAL SYMMETRIC MATRICES.
HERMIT IAN MATRICES.
SINGULAR VALUES AND SINGULAR VALUE DECOMPOSITION - EXTREMA OF QUADRATIC
FORMS.
VECTOR AND MATRIX DIFFERENTIATION.
LINEAR ALGEBRA (MSC-STAT)(2030617)
________________________________________________
MOST POWERFUL TEST - FUNDAMENTAL NOTIONS OF HYPOTHESIS - TESTING
RANDOMIZED AND NON-RANDOMIZED TESTS.
MOST POWERFUL TESTS - THE NEYMAN-PEARSON FUNDAMENTAL LEMMA.
UNIFORMALLY MOST POWERFUL TEST - UMP TEST - DISTRIBUTIONS WITH MONOTONE
LIKELIHOOD RATIO - GENERALIZATION OF THE FUNDAMENTAL LEMMA.
UMP TEST FOR TWO SIDED HYPOTHESIS.
UNBIASED AND UMPU TEST - UNBIASED NESS FOR HYPOTHESIS TESTING - UMPU
TESTS FOR ONE PARAMETER EXPONENTIAL FAMILY - SIMILAR TEST - TEST WITH
NEYMANN - STRUCTURE - LIKELIHOOD RATIO TEST.
RELATIONSHIP BETWEEN TESTING OF HYPOTHESIS AND CONFIDENCE INTERVAL.
SEQUENTIAL PROBABILITY RATIO TEST - SEQUENTIAL PROBABILITY RATIO TEST -
PROPERTIES OF SPRIT - EFFICIENCY OF THE SPRIT.
ECONOMY OF SEQUENTIAL TESTING - THE FUNDAMENTAL IDENTIFY OF THE SPRIT.
NON-PARAMETRIC TEST - SINGLE SAMPLE PROBLEMS - KOLMOGROV - SIMIRNOV TEST.
THE SIGN TEST - THE WILCOXON SIGNED RANKS TEST - TWO SAMPLE PROBLEMS -
KOLMOGRO -SIMIRNOV TWO SAMPLE TEST.
THE MEDIAN TEST.
THE MANN - WHITNEY - WILCOXON TEST.
STATISTICAL INFERENCE(2030618)
ESTIMATORS OF TOTAL - PARTIAL AND MULTIPLE CORRELATION COEFFICIENT AND
THEIR NULL DISTRIBUTIONS TEST FOR TOTAL - PARTIAL AND MULTIPLE CORRELATION
COEFFICIENT.
TEST FOR TOTAL - PARTIAL AND MULTIPLE REGRESSION COEFFICIENTS.
DISTRIBUTION OF SAMPLE DISPERSION MATRIX - WISHART DISTRIBUTION.
PROPERTIES - HOTEL LING`S T2 AND MAHALANOBIS OF D2 STATISTICS - THEIR NULL
DISTRIBUTIONS.
TEST FOR MEAN VECTOR OF ONE AND TWO MULTIVARIATE NORMAL POPULATIONS
BASED ON T2 (OR D2) DISTRIBUTION - CLASSIFICATION PROBLEM.
CLASSIFICATION OF TWO MULTIVARIATE NORMAL POPULATIONS - BAYE`S PROCEDURE
- CALCULATION OF THE PROBABILITIES OF MISCLASSIFICATION.
DISCRIMINATE ANALYSIS - FISHERS DISCRIMINATE FUNCTION - TEST FOR ASSIGNED
DISCRIMINATE FUNCTION.
CANONICAL CORRELATIONS AND CANONICAL VARIANTS.
PRINCIPAL COMPONENT ANALYSIS - EXTRACTION.
PROPERTIES - FACTOR ANALYSIS - ORTHOGONAL FACTOR MODEL - PRINCIPAL
COMPONENT SOLUTION TO FACTOR MODEL.
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