JAM ACHIEVER COURSE Mathematical Statistics (2023)

Eduncle
IIT JAM
3

This Course is designed and developed by a team of Highly Experienced and Qualified Faculties. It covers entire Syllabus and promise to make Student full prepared to give IIT JAM Exam with confidence.

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Highlight Section

  • 1800 Practice Questions & 5 PSPs with Solutions
  • Complete Syllabus Covered
  • Easy to Understand Format
  • Highly Experienced and Qualified Faculty
  • Result Oriented Study Material

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Course Structure

The Curriculum Section of  this Course covers the following Content :

  • 15 Units of Theory
  • 15 Unit wise Practice Question Papers with Solutions (USPs)
  • 5 Volume wise Practice Question Papers with Solutions (VSPs)
  • 10 Full Length Model Solved Papers (MSPs)
  • 5 Previous Year Solved Papers (PSPs)- In Online Mode Only

Module: IIT JAM MS UNIT (1-15) 2019-20

  • Subject: Mathematical Statistics (MS)
    • Section 1: Unit - 1

        Attachments 1: Introduction

        Attachments 2: Sequence

        Attachments 3: CONVERGENT AND DIVERGENT SEQUENCES

        Attachments 4: BOUNDED AND UNBOUNDED SEQUENCE

        Attachments 5: MONOTONE SEQUENCE

        Attachments 6: INFINITE SERIES

        Attachments 7: UPPER AND LOWER LIMITS

        Attachments 8: CONVERGENCE CRITERIA FOR SEQUENCES OF REAL NUMBERS

        Attachments 9: SUBSEQUENCE

        Attachments 10: CAUCHY SEQUENCE

        Attachments 11: ABSOLUTE AND CONDITIONAL CONVERGENCE

        Attachments 12: TESTS OF CONVERGENCE OF SERIES

        Attachments 13: CONVERGENCE OF THE INFINITE INTEGRAL

        Attachments 14: ALTERNATING SERIES

    • Section 2: Unit - 2

        Attachments 1: Introduction

        Attachments 2: LIMIT OF A FUNCTION OF ONE VARIABLE

        Attachments 3: CONTINUOUS FUNCTIONS OF ONE VARIABLE

        Attachments 4: DERIVABILITY OF A FUNCTION OF ONE VARIABLE

        Attachments 5: INTERMEDIATE VALUE PROPERTY

        Attachments 6: FUNCTIONS OF TWO VARIABLES

        Attachments 7: LIMIT OF A FUNCTION OF TWO VARIABLES

        Attachments 8: CONTINUITY OF A FUNCTION OF TWO VARIABLES

        Attachments 9: PARTIAL DERIVATIVES

        Attachments 10: DIFFERENTIABILITY OF TWO VARIABLES

    • Section 3: Unit - 3

        Attachments 1: ROLLE’S THEOREM STATEMENT

        Attachments 2: MEAN VALUE THEOREM

        Attachments 3: TAYLOR’S THEOREM

        Attachments 4: MAXIMA AND MINIMA OF ONE VARIABLE

        Attachments 5: INDETERMINATE FORMS AND LHOSPITALS RULE

        Attachments 6: MAXIMA AND MINIMA OF FUNCTIONS OF TWO VARIABLES

        Attachments 7: METHOD OF LAGRANGE MULTIPLIER

    • Section 4: Unit - 4

        Attachments 1: ANTIDERIVATIVES - DIFFERENTIATION IN REVERSE

        Attachments 2: DEFINITE INTEGRALS AND THEIR PROPERTIES

        Attachments 3: DIFFERENTIATION UNDER THE INTEGRAL SIGN

        Attachments 4: FUNDAMENTAL THEOREM OF CALCULUS

        Attachments 5: DOUBLE INTEGRAL

        Attachments 6: CHANGE OF ORDER OF INTEGRATION

        Attachments 7: TRIPLE INTEGRALS

        Attachments 8: SURFACE AREA

        Attachments 9: EVALUATION OF VOLUMES

        Attachments 10: ARC LENGTH

    • Section 5: Unit - 5

        Attachments 1: VECTOR SPACES

        Attachments 2: LINEAR COMBINATION

        Attachments 3: SPANNING SET

        Attachments 4: SUBSPACES

        Attachments 5: LINEAR DEPENDENCE AND INDEPENDENCE

        Attachments 6: BASIS AND DIMENSION

        Attachments 7: LINEAR TRANSFORMATION

        Attachments 8: VECTOR SPACE ISOMORPHISM

        Attachments 9: KERNEL AND IMAGE OF A LINEAR MAPPING

        Attachments 10: RANK AND NULLITY OF A LINEAR MAPPING

        Attachments 11: RANK-NULLITY THEOREM

    • Section 6: Unit - 6

        Attachments 1: MATRICES

        Attachments 2: RANK OF MATRIX

        Attachments 3: INVERSE OF A MATRIX

        Attachments 4: DETERMINANTS

        Attachments 5: SYSTEM OF LINEAR EQUATIONS

        Attachments 6: CONSISTENT AND IN-CONSISTENT NON-HOMOGENEOUS LINEAR EQUATIONS

        Attachments 7: EIGEN VALUES AND EIGEN VECTORS

    • Section 7: Unit - 7

        Attachments 1: INTRODUCTION

        Attachments 2: CLASSICAL APPROACH TO PROBABILITY

        Attachments 3: AXIOMATIC APPROACH TO PROBABILITY

        Attachments 4: ADDITION THEOREMS ON PROBABILITY

        Attachments 5: CONDITIONAL PROBABILITY

        Attachments 6: MULTIPLICATION THEOREMS ON PROBABILITY

        Attachments 7: INDEPENDENT EVENTS

        Attachments 8: THE LAW OF TOTAL PROBABILITY

        Attachments 9: BAYES RULE

    • Section 8: Unit - 8

        Attachments 1: RANDOM VARIABLE

        Attachments 2: DISTRIBUTION FUNCTION

        Attachments 3: DISCRETE RANDOM VARIABLE

        Attachments 4: CONTINUOUS RANDOM VARIABLE

        Attachments 5: THE DISTRIBUTION OF A FUNCTION OF A RANDOM VARIABLE

        Attachments 6: CUMULATIVE DISTRIBUTION FUNCTIONS

    • Section 9: Unit - 9

        Attachments 1: MATHEMATICAL EXPECTATION

        Attachments 2: COVARIANCE, VARIANCE OF SUMS, AND CORRELATIONS

        Attachments 3: CONDITIONAL EXPECTATION

        Attachments 4: THE VARIANCE AND STANDARD DEVIATION

        Attachments 5: MOMENTS

        Attachments 6: MOMENT GENERATING FUNCTIONS

        Attachments 7: CHARACTERISTIC FUNCTIONS

        Attachments 8: CHEBYSHEVS INEQUALITY

    • Section 10: Unit - 10

        Attachments 1: THE BERNOULLI AND BINOMIAL RANDOM VARIABLES

        Attachments 2: THE POISSON RANDOM VARIABLE

        Attachments 3: THE NEGATIVE BINOMIAL RANDOM VARIABLE

        Attachments 4: THE HYPERGEOMETRIC RANDOM VARIABLE

        Attachments 5: THE ZETA (OR ZIPF) DISTRIBUTION

        Attachments 6: EXPECTATION AND VARIANCE OF CONTINUOUS RANDOM VARIABLES

        Attachments 7: THE UNIFORM RANDOM VARIABLE

        Attachments 8: NORMAL RANDOM VARIABLES

        Attachments 9: EXPONENTIAL RANDOM VARIABLES

        Attachments 10: THE GAMMA DISTRIBUTION

        Attachments 11: THE WEIBULL DISTRIBUTION

        Attachments 12: THE CAUCHY DISTRIBUTION

        Attachments 13: THE BETA DISTRIBUTION

        Attachments 14: THE NORMAL APPROXIMATION TO THE BINOMIAL DISTRIBUTION

        Attachments 15: THE DEMOIVRE-LAPLACE LIMIT THEOREM

    • Section 11: Unit - 11

        Attachments 1: JOINT PROBABILITY LAW

        Attachments 2: JOINT PROBABILITY MASS FUNCTION AND MARGINAL AND CONDITIONAL

        Attachments 3: JOINT PROBABILITY DISTRIBUTION FUNCTION

        Attachments 4: DISCRETE DISTRIBUTION FUNCTIONS

        Attachments 5: MARGINAL DISTRIBUTION FUNCTION

        Attachments 6: JOINT DENSITY FUNCTION, MARGINAL DENSITY FUNCTIONS

        Attachments 7: CONDITIONAL DISTRIBUTIONS

        Attachments 8: INDEPENDENT RANDOM VARIABLES

        Attachments 9: REGRESSION

        Attachments 10: PEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT

        Attachments 11: PEARSONS CORRELATION AND LEAST SQUARES REGRESSION ANALYSIS

        Attachments 12: JOINT MOMENT GENERATING FUNCTION

    • Section 12: Unit - 12

        Attachments 1: EXACT SAMPLING DISTRIBUTIONS (CHI-SQUARE DISTRIBUTION)

        Attachments 2: M.G.G. of CHI-SQUARE DISTRIBUTION

        Attachments 3: CUMULANT GENERATING FUNCTION OF CHI-SQUARE DISTRIBUTIONS

        Attachments 4: LIMITING FORM OF X2 DISTRIBUTION FOR LARGE DEGREES OF FREEDOM

        Attachments 5: CHI-SQUARE PROBABILITY CURVE

        Attachments 6: CHI-SQUARE TEST OF GOODNESS OF FIT

        Attachments 7: NON-CENTRAL CHI-SQUARE DISTRIBUTIONS

        Attachments 8: STUDENTS t DISTRIBUTION

        Attachments 9: MOMENT GENERATING FUNCTION OF t-DISTRIBUTION

        Attachments 10: APPLICATIONS OF t-DISTRIBUTION

        Attachments 11: NON-CENTRAL t-DISTRIBUTION

        Attachments 12: F-STATISTIC

        Attachments 13: MODE AND POINTS OF INFLECTION OF F-DISTRIBUTION

        Attachments 14: APPLICATIONS OF F-DISTRIBUTION

        Attachments 15: RELATION BETWEEN t AND F-DISTRIBUTIONS

        Attachments 16: RELATION BETWEEN F AND CHI-SQUARE

        Attachments 17: NON-CENTRAL F-DISTRIBUTION

    • Section 13: Unit - 13

        Attachments 1: INTRODUCTION

        Attachments 2: CHEBYSHEVS INEQUALITY AND THE WEAK LAW OF LARGE NUMBERS

        Attachments 3: THE CENTRAL LIMIT THEOREM

        Attachments 4: THE STRONG LAW OF LARGE NUMBERS

    • Section 14: Unit - 14

        Attachments 1: INTRODUCTION

        Attachments 2: CONSISTENCY

        Attachments 3: UNBIASEDNESS

        Attachments 4: EFFICIENT ESTIMATORS

        Attachments 5: MINIMUM VARIANCE UNBIASED (M.V.U.) ESTIMATORS

        Attachments 6: SUFFICIENCY

        Attachments 7: COMPLETENESS

        Attachments 8: FACTORIZATION THEOREM

        Attachments 9: CRAMER-RAO INEQUALITY

        Attachments 10: RAO-BLACKWELLISATON

        Attachments 11: LEHMANN-SCHEFFE THEOREM

        Attachments 12: METHOD OF MAXIMUM LIKELIHOOD ESTIMATION

        Attachments 13: METHOD OF MOMENTS

        Attachments 14: CONFIDENCE INTERVAL AND CONFIDENCE LIMITS

        Attachments 15: CONFIDENCE INTERVALS FOR ONE PARAMETER EXPONENTIAL DISTRIBUTIONS

    • Section 15: Unit - 15

        Attachments 1: INTRODUCTION

        Attachments 2: BASIC CONCEPTS OF HYPOTHESIS TESTING

        Attachments 3: TEST OF HYPOTHESIS ABOUT POPULATION MEAN MYU

        Attachments 4: STEPS IN SOLVING TESTING OF HYPOTHESIS PROBLEM

        Attachments 5: OPTIMUM TEST UNDER DIFFERENT SITUATIONS

        Attachments 6: NEYMAN-PEARSON LEMMA FOR TESTING SIMPLE AND COMPOSITE HYPOTHESES

        Attachments 7: LIKELIHOOD RATIO TESTS

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