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# Mathematical & Statistical Techniques-II FYBCOM Semester II

Mathematical & Statistical Techniques-II FYBCOM Semester II

## Description

Mathematical & Statistical Techniques-II

FYBCOM Semester II

Content:

MATHEMATICS (40 MARKS)

Unit - I : Functions, Derivatives and Their Applications (15 Lec.)
(a) Concept of Real Functions : Constant function, linear function, xn , ex, ax, log x.
Demand, Supply, Total Revenue, Average Revenue, Total cost, Average Cost and Profit Function. Equilibrium Point, Break-even Point.
(b) Derivative of Functions :
l Derivative as rate measure, Derivative of xn , ex, ax, log x.
l Rules of derivatives: Scalar multiplication, sum, difference, product, quotient (Statements only), Simple problems. Second order derivatives.
l Applications: Marginal Cost, Marginal Revenue, Elasticity of Demand. Maxima and Minima for functions in Economics and Commerce.
(Examination Questions on this unit should be application oriented only.)

Unit - II : Interest and Annuity (15 Lec.)
(a) Interest: Simple Interest, Compound Interest (Nominal & Effective Rate of Interest),. Calculations involving upto 4 time periods.
(b) Annuity: Annuity Immediate and its Present value, Future value. Equated Monthly Installments (EMI) using reducing balance method & amortization of loans. Stated Annual Rate & Affective Annual Rate Perpetuity and its present value. Simple problems involving up to 4 time periods.

STATISTICS (60 MARKS)

Unit - III : Bivariate Linear Correlation and Regression (15 Lec.)
(a) Correlation Analysis : Meaning, Types of Correlation, Determination of Correlation: Scatter Diagram, Karl Pearson’s Method of Correlation Coefficient (excluding Bivariate Frequency Distribution Table) and Spearman’s Rank Correlation Coefficient.
(b) Regression Analysis : Meaning, Concept of Regression Equations, Slope of the Regression Line and its Interpretation. Regression Coefficients (excluding Bivariate Frequency Distribution Table), Relationship between Coefficient of Correlation and Regression Coefficients, Finding the equations of Regression lines by method of Least Squares.

Unit - IV : Time Series and Index Numbers (15 Lec.)
(a) Time Series : Concepts and Components of a Time Series. Representation of trend by Freehand Curve Method, Estimation of Trend using Moving Average Method and Least Squares Method (Linear Trend only). Estimation of Seasonal Component using Simple Arithmetic Mean for Additive Model only (For Trend free data only). Concept of Forecasting using Least Squares Method.
(b) Index Numbers : Concept and usage of Index numbers, Types of Index numbers, Aggregate and Relative Index Numbers, Lasperye’s, Paasche’s, Dorbisch-Bowley’s, Marshall-Edgeworth and Fisher’s ideal index numbers, Test of Consistency: Time Reversal Test and Factor Reversal Test. Chain Base Index Nos. Shifting of Base year. Cost of Living Index Numbers, Concept of Real Income, Concept of Wholesale Price Index Number. (Examples on missing values should not be taken)

Unit - V : Elementary Probability Distributions (15 Lec.)
Probability Distributions:
l Discrete Probability Distribution : Binomial, Poisson (Properties and applications only, no derivations are expected)
l Continuous Probability Distribution : Normal Distribution. (Properties and applications only, no derivations are expected)

Tutorial :
Two tutorials to be conducted on each unit i.e. 10 tutorials per semester. At the end of each semester one Tutorial assignment of 10 marks should be given.