Semester - I Syllabus

Osmania University

B.Sc. I Year, I Semester (CBCS): Statistics Syllabus

Paper-I: Descriptive Statistics and Probability (DSC-2A)

(4 HPW with 4 Credits and 100 Marks)

UNIT –I

Descriptive Statistics: Concept of primary and secondary data. Methods of collection and editing of primary data. Designing a questionnaire and a schedule. Sources and editing of secondary data. Classification and tabulation of data. Measures of central tendency (mean, median, mode, geometric mean and harmonic mean) with simple applications. Absolute and relative measures of dispersion (range, quartile deviation, mean deviation and standard deviation) with simple applications. Importance of moments, central and non-central moments, and their interrelationships, Sheppard’s corrections for moments for grouped data. Measures of Skewness based on quartiles and moments and kurtosis based on moments with real life examples.

UNIT-II

Probability: Basic concepts in probability—deterministic and random experiments, trail, outcome, sample space, event, and operations of events, mutually exclusive and exhaustive events, and equally likely and favorable outcomes with examples. Mathematical, statistical and axiomatic definitions of probability with merits and demerits. Properties of probability based on axiomatic definition. Conditional probability and independence of events. Addition and multiplication theorems for n events. Boole’s inequality and Bayes’ theorem. Problems on probability using counting methods and theorems.

UNIT-III

Random Variables: Definition of random variable, discrete and continuous random variables, functions of random variables, probability mass function and probability density function with illustrations. Distribution function and its properties. Transformation of one-dimensional random variable (simple 1-1 functions only).Notion of  bivariate random variable, bivariate distribution and statement of its properties. Joint, marginal and conditional distributions. Independence of random variables.

UNIT-IV

Mathematical Expectation: Mathematical expectation of a function of a random variable. Raw and central moments and covariance using mathematical expectation with examples. Addition and multiplication theorems of expectation. Definition of moment generating function (m.g.f), cumulant generating function (c.g.f), probability generating function (p.g.f) and characteristic function (c.f) and statements of their properties with applications. Chebyshev’s, and Cauchy-Schwartz’s inequalities and their applications.

List of reference books:

1.Charles M.Grinstead and Laurie Snell,J:Introduction to Probability,American Mathematical Society

2.Willam Feller: Introduction to Probability theory and its applications. Volume –I, Wiley

3.V.K.Kapoor and S.C.Gupta: Fundamentals of Mathematical Statistics, Sultan Chand&Sons, New Delhi

4. GoonAM,GuptaMK,Das Gupta B : Fundamentals of Statistics , Vol-I, the World Press Pvt.Ltd.,Kolakota.

5. M.JaganMohan Rao and Papa Rao: A Text book of Statistics Paper-I.

Practical Paper – I (with 2 HPW, Credits 1 and Marks 25)

1. Basics of Excel- data entry, editing and saving, establishing and copying formulae, built in

Functions in excel, copy and paste and exporting to MS word document. (Not for The Examination).

2. Graphical presentation of data (Histogram, frequency polygon, Ogives).

3. Graphical presentation of data (Histogram, frequency polygon, Ogives) using MS Excel

4. Diagrammatic presentation of data (Bar and Pie).

5. Diagrammatic presentation of data (Bar and Pie) using MS Excel

6. Computation of non-central and central moments – Sheppard’s corrections for grouped data.

7. Computation of coefficients of Skewness and Kurtosis -Karl Pearson’s and Bowley’s b1 and b2.

8. Computation of Measures of central tendency, dispersion, Coefficient of Variation and coefficients of Skewness, Kurtosis using MS Excel.