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.
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