Attend demo classes on BSc Statistics - 3 online statistics tuitions

Attend demo classes on BSc Statistics - 3 online statistics tuitions

on 20 July 2015 at 6:15 pm ( 3 days )   

Registration free at https://www.bijmathiq.com/

Unit I

Design of Sample Surveys 

Concepts of population, sample, sampling unit, parameter, statistic, sample frame and standard error. Principal steps in sample surveys need for sampling, censusversus sample surveys, sampling and nonsampling errors, sources and treatment of nonsampling errors, advantages and limitations of sampling. Types of sampling: Subjective, probability and mixed sampling methods. Methods of drawing random samples with and without replacement. Estimates of population mean,total, and proportion, their variances and the estimates of variances in the following methods.

(i) SRSWR and SRSWOR

(ii) Stratified random sampling with proportional and Neyman allocation, and

(iii) Systematic sampling when N= nk.

Comparison of relative efficiencies. Advantages and disadvantages of above methods of sampling.

Unit II

Analysis of Variance and Design of Experiments 

Concept of GaussMarkoff ,linear modelwith examples, statement of Cochran’s theorem, ANOVA – oneway,twoway.classifications with one observation per cellExpectation of various sums of squares, Statistical l analysis,Importance and applications of design of experiments. 

Principles of experimentation, Analysis of Completely randomized Design (C.R.D), Randomized Block Design (R.B.D) and Latin Square Design (L.S.D) including one missing observation, expectation of various .sum of squares. Comparison of the efficiencies of above designs.

Unit III

Time series:

Time series and its components with illustrations, additive, multiplicative and mixed models. Determination of trend by least squares, moving average methods. Growth curves and their fittingwith reference to Modified exponential, Gompertz and Logistic curves. Determination of seasonal indices by Ratio to moving average, ratio to trend and link relative methods.Index Numbers: Concept,construction, uses and limitations of simple and weighted index numbers. Laspeyer’s, Paasche’s and Fisher’s index numbers, criterion of a good index numbers, problems involved in the construction of index numbers. Fisher’s index as ideal index number. Fixed and chain base index numbers. Cost of living index numbers and wholesale price index numbers. Base shifting, splicing and deflation of index numbers.Official Statistics: Functions and organization of CSO and NSSO. Agricultural Statistics, area and yield statistics. National Income and its computation, utility and

difficulties in estimation of national income.

Unit IV

Vital statistics: 

Introduction, definition and uses of vital statistics. Sources of vital statistics, registration method and census method. Rates and ratios, Crude death rates, age specific death rate, standardized death rates, crude birth rate, age specific fertility rate, general fertility rate, total fertility rate. Measurement of population growth, crude rate of natural increasePearl’s vital index. Gross reproductive rate sand Net reproductive rate, Life tables, construction and uses of life tables and Abridged life tables. Demand Analysis: Introduction. Demand and supply, price elasticity of supply and demand. Methods of determining demand and supply curves, Leontief’s ,Pigous’s methods of determining dema.

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1. Get tutoring from well qualified and experianced faculty .
2. Get unlimited access to live sessions recording videos at free .
3. Clear explanation of concepts using various mathematical tools ( wherever required )
4. Covers maximum number of examples 
5. take online quiz tests ( 10+ with explanation video  for each test ) at free
6. Access  self pace tuitions (30 + videos )
7. Handwritten material provided 
8. PPT's
9. Get full support from BijMathIQ - Online Maths Tuitions .

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Attend demo classes on BSc Maths - 3 Online MathsTuitions

BSc Maths - 3 Online MathsTuitions
for IIT - JAM Coaching

Attend free demo Live classes are scheduled on 23 July 2015 at 6:15 am 

Register at Website : https://www.bijmathiq.com/
Part-A
Vector Space

Learnig Objectives

•  Binary Operations , vectors ,vector addition and scalar multiplication
•  Definition of vector space  and Subspaces
•  Linear combination , span , LD , LI and basis
•  Dimension of vector space , dimension theorem
•  Linear transformations and its matrix representation
•  Sylvester's law
•  Eigen values and vectors , caylay-hamilton theorem , diagonalization 
•  Inner product , euclidean and unitary spaces , norm of a vector , schwartz's inequality 
•  orthogonality , orthonormal sets and gram-schmidt process

Syllabus

Vectoer spaces - general properties . Subspaces , linear combination ,spanning , basis , finite dimensional vector space , linear transformations , rank-nullity theorems , matrix representation of linear transformations  and its characteristics sylvester's law of nullity,characteristic vlues and vectors , caylay - hamilton theorem ,diagonalization.Inner product spaces ,euclidean and unitary spaces , norm , schwartz's inequality , orthogonality, orthonormal set and gram-schmidt orthogonalization process .

Learning out comes

Student will

• Learn how the binary operations will work on vector spaces , when does the non empty subset of a vector space becomes the subspace of the vector space .
• learn about linear combinations and it spans the vector space and form the basis for vector space , identifying the dimension of the vector space .
• Study about the dimension theorem proof and will verify  and get the dimension of the vector spaces .
• learn about linear transformations - properties and characterisrics , matrix representations .Sylvester's law of nullity .
• learn about eigen values and eigen vectors - properties and charecterics eigen values and eigen vectors  and caylay hamilton theorem - its verification and finding Inverse of A and powers of A .
• Study and learn about the norm ( length) of the vectors , ineer product spaces , euclidean and unitary spaces -their properties and characteristics -schwartz's inequality .
• Orthogonalization of vectors and orthionormal sets and gran-schmidt's process of orthogonalization .

Part - B     Multiple Integrals & Vector Calculus

Learning Objectives :

• Line and multiple integrals  , limit form and existance .
• Double integral and defining over the region R , change of order of integration and change of variables , double integrals in polar coordinates .
• Triple integrals and defining over the volume V.
• Applications of double and triple integrals .
• Vector calculus ( differentiation and integration ).
• Vector differential operator , Gradient ,Divergence and Curl and their applications , vector identities .
• Vector integration - Line , Surface  and Volume integrals
• Vector integral theorems - Green's , Gauss and Stoke's theorem and their verifications .

Syllabus 

Introduction to multiple integrals : concept of plane and curve ,line integrals , sufficient condition for existance of line integrals , The area of a subset of R^2 ,Calculation of double integrals , jordan curve , area , change of order integration and change of variables , lengths of curve , surface areas , integral expression for the length of  a curve .

Vector Calculus ( Differentiation and Integration ) :Ordinary derivatives of vectors , space curves , continuity and differentiability . Gradeient , Divergence and curl operators - identities .Vector integral theorems , Green's , Gauss and Stoke's theorems and their verifications .

Learning out comes:

Student will

• Learn about the concept and how to define the  double integrals over the region R .
• How to evaluate the double integrals by changing the order of integration and by change of variable .
• Learn to calculate the double integrals in polar coordinates and Areas enclosed by the closed curves .
• How to evaluate the triple integrals over the volumes .
• Learn about the vector differentiation and integration and vector differential operator, Gradient ,Divergence and Curl and vector identities 
• Vector integration : Evaluation of Line integrals along the curves , surface interals over the surfaces and volume integrals over the volumes .
• vector integral theorems - Green's , Gauss and Stoke's theorems and their verifications.

BijMathIQ - Online Maths Tuitions - great advantages for students
1) Get tutoring from most experianced and efficient faculty.
2) Students can get unlimited access his live class session recording videos , until the completion of final exams .
3)Explanation of every concepts verious technologies like Geogebra ( Graphical presentations ) , Mathematics , MatLab ,SciLab and MSExcel (Probability & Statistics ) .
4) Take online test and report ,check and verify by accessing  the explanation video of his online test .
5) Covers the maximum number of problems on each topic.
6) Student can rise , ask and clarifies his doubts at the same time in the live class ( is also recorded in the video ).
7) Live chat box facility in liva class session
8) Web cam for the student is optional .
9) Hand written notes will be provided ( if required ) .
and many more ....
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Engineering Mathematics - 1 Online Maths Tuitions

Engineering Mathematics - 1 
Online Maths Tuitions

Live tuitions through online virtual class room will start very soon 

SYLLABUS

Learning Objectives & Outcomes:

Student will

• learn about the matrices , Rank and normal forms , Solving the system of linear equations , eigen values and eigen vectors , their properties ,caylay hamilton theorem .Diagonalization of the matrix , reduction of QF to CF and characteristics .
• Study about the mean value theorems :Rolle's , Lagrange's , cauchy's mean value theorems and generalized mean value theorems and their verifications . Fuctions of several variables : Brief introduction to partial derivatives , Jacobian , functional dependendence ,finding Maxima And Minima and also using Lagrangian method of undetermined coefficients .
• Study about Beta-Gamma functions , relation between them and their properties , evaluation of improper integrals .                               Multiple Integrals : Evaluation of double and triple integrals and their applications .
• learn how to solve the differential equations , solving first order and first degree ODE and their formation ,applications .Solving higher order DE i.e. finding CF and PI of various input functions .
• Syudy about the Laplace Transforms and Inverse Laplace Transforms  its properties . Application of LT to solve differential equations (IVP).

SYLLABUS Contents :

1. Matrices
2. Differential Calculus
3. Improper Integrals and Beta-Gamma functions
4. Differential Equations
5. Laplace transforms 

( Contents may be different , depending on respective University ,but finally all engineering mathematics subjects for engineering students same ) .

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IIT - JAM Mathematics Coaching

IIT-JAM ( MATHEMATICS (MA) )

SEQUENCES, SERIES : Sequences and Series of real numbers: Sequences and series of real numbers. Convergent and divergent sequences, bounded and monotone sequences, Convergence criteria for sequences of real numbers, Cauchy sequences, absolute and conditional convergence; Tests of convergence for series of positive terms - comparison test, ratio test, root test, Leibnitz test for convergence of alternating series.

DIFFERENTIAL CALCULUS Functions of one variable: limit, continuity, differentiation, Rolle's Theorem, Mean value theorem. Taylor's theorem. Maxima and minima. Functions of two real variable: limit, continuity, partial derivatives, differentiability, maxima and minima. Method of Lagrange multipliers, Homogeneous functions including Euler's theorem.

Integral Calculus: Integration as the inverse process of differentiation, definite integrals and their properties, Fundamental theorem of integral calculus. Double and triple integrals, change of order of integration. Calculating surface areas and volumes using double integrals and applications. Calculating volumes using triple integrals and applications.

Differential Equations: Ordinary differential equations of the first order of the form y'=f(x,y). Bernoulli's equation, exact differential equations, integrating factor, Orthogonal trajectories, Homogeneous differential equations-separable solutions, Linear differential equations of second and higher order with constant coefficients, method of variation of parameters. Cauchy- Euler equation.

Vector Calculus: Scalar and vector fields, gradient, divergence, curl and Laplacian. Scalar line integrals and vector line integrals, scalar surface integrals and vector surface integrals, Green's, Stokes and Gauss theorems and their applications.

Group Theory: Groups, subgroups, Abelian groups, non-abelian groups, cyclic groups, permutation groups; Normal subgroups, Lagrange's Theorem for finite groups, group homomorphisms and basic concepts of quotient groups (only group theory).

Linear Algebra: Vector spaces, Linear dependence of vectors, basis, dimension, linear transformations, matrix representation with respect to an ordered basis, Range space and null space, rank-nullity theorem; Rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions. Eigenvalues and eigenvectors. Cayley-Hamilton theorem. Symmetric, skewsymmetric, hermitian, skew-hermitian, orthogonal and unitary matrices.

Real Analysis: Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets; completeness of R, Power series (of real variable) including Taylor's and Maclaurin's, domain of convergence, term-wise differentiation and integration of power series. 

Great benifits from  BijMathIQ - Online Maths Tuitions

1. Get tutoring from well qualified and experianced faculty .
2. Get unlimited access to live sessions recording videos at free .
3. Clear explanation of concepts using various mathematical tools ( wherever required )
4. Covers maximum number of examples 
5. take online quiz tests ( 10+ with explanation video  for each test ) at free
6. Access  self pace tuitions (30 + videos )
7. Handwritten material provided 
8. PPT's
9. Get full support from BijMathIQ - Online Maths Tuitions .

For demo and further details please contact : + 91 9490875895

                  (OR) 

Email Id ; bijmathiq@gmail.com

WebSite : https://www.bijmathiq.com

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IIT-JAM coaching for Mathematical Statistics

IIT -JAM
MATHEMATICAL STATISTICS (MS) coaching

The Mathematical Statistics (MS) test paper comprisesof Mathematics (40% weightage) and Statistics (60%weightage).

Mathematics:

Sequences and Series: Convergence of sequences of real numbers, Comparison,root and ratio tests for convergence of series of real numbers.

Differential Calculus: Limits, continuity and differentiability of functions of one and two variables. Rolle's theorem, mean value theorems, Taylor's theorem, indeterminate forms, maxima and minima of functions of one and two variables.

Integral Calculus: Fundamental theorems of integral calculus. Double and triple integrals, applications of definite integrals, arc lengths, areas and volumes.

Matrices: Rank, inverse of a matrix. systems of linear equations. Linear transformations, eigenvalues and eigenvectors. CayleyHamilton theorem , symmetric, skewsymmetric and orthogonal matrices.

Differential Equations: Ordinary differential equations of the first order of the form y' = f(x,y). Linear differential equations of the second order with constant coefficients. 

Statistics 

Probability: Axiomatic definition of probability and properties, conditional probability, multiplication rule. Theorem of total probability. Bayes' theorem and independence of events.

Random Variables: Probability mass function, probability density function and cumulative distribution functions, distribution of a function of a random variable. Mathematical expectation, moments and moment generating function. Chebyshev's inequality.

Standard Distributions: Binomial, negative binomial, geometric, Poisson, hypergeometric, uniform, exponential, gamma, beta and normal distributions. Poisson and normal approximations of a binomial distribution.

Joint Distributions: Joint, marginal and conditional distributions. Distribution of functions of random variables. Product moments, correlation, simple linear regression. Independence of random variables. 

Sampling distributions: Chisquare, t and F distributions, and their properties.

Limit Theorems: Weak law of large numbers. Central limit theorem (i.i.d.with finite variance case only).

Estimation: Unbiasedness, consistency and efficiency of estimators, method of moments and method of maximum likelihood. Sufficiency, factorization theorem. Completeness, RaoBlackwell and LehmannScheffe theorems, uniformly minimum variance unbiased estimators. RaoCramer inequality. Confidence intervals for the parameters of univariate normal, two independent normal, and one parameter exponential distributions.

Testing of Hypotheses: Basic concepts, applications of  NeymanPearson Lemma for testing simple and composite hypotheses. Likelihood ratio tests for parameters of univariate normal distribution.

Great benifits from  BijMathIQ - Online Maths Tuitions

1. Get tutoring from well qualified and experianced faculty .
2. Get unlimited access to live sessions recording videos at free .
3. Clear explanation of concepts using various mathematical tools ( wherever required )
4. Covers maximum number of examples 
5. take online quiz tests ( 10+ with explanation video  for each test ) at free
6. Access  self pace tuitions (30 + videos )
7. Handwritten material provided 
8. PPT's
9. Get full support from BijMathIQ - Online Maths Tuitions .

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