Descriptive Statistics and Probability Distributions

SHIVAJI UNIVERSITY, KOLHAPUR
School of Nanoscience and Technology
(5 year integrated multidisciplinary 10 semester course)
Semester-II
SYLLABUS
Title of the paper: Descriptive Statistics and Probability Distributions
Credits: 3

Lectures 45
1 Unit- I
Meaning and scope of statistics in industry and physical sciences,
population and sample, census method, sampling method.
Primary and secondary data, ungrouped and grouped data,
qualitative data (attributes) and quantitative data (variables),
frequency distribution. Histogram, frequency curve, Box plot.
Concept of central tendency, criteria for good measures of central
tendency. Arithmetic mean, median, mode and their properties,
Computations of mean, median and mode for ungrouped and
grouped data.
08
2 Unit- II
Concept of dispersion, measures of dispersion, absolute and
relative measures of dispersion, range, mean deviation, standard
deviation and their relative measures. Variance, coefficient of
variation. Concepts and measures of skewness and kurtosis
Correlation and regression (for ungrouped data) : Bivariate data,
concept of correlation, scatter diagram, Karl Pearson’s coefficient
of correlation, Spearman’s Rank Correlation coefficient.
Regression: concept, lines of regression, least square method,
regression coefficients, relation between correlation and
regression coefficients.
12
3 Unit- III
Concept of experiment with random outcome, sample
space, finite and countably infinite sample space, discrete sample
space, events, types of events, power set, Classical (apriori)
definition of probability of an event, axiomatic definition of
probability.
Theorems on probability: i) P(Φ) = 0, ii) P(Ac) = 1 – P(A)
iii) P(A U B) = P(A) + P(B) – P(A ∩ B), iv) If A is subset of B then
P(A) ≤ P(B)
v) 0 ≤ P(A ∩ B) ≤ P(A) ≤ P(A U B) ≤ P(A) + P(B) simple
examples.Conditional probability and independence of events:
Independence of two events, properties and examples. Definition
12
Paper No: SNST-204T
Total Marks: 100
(80+20)
of conditional probability, Bayes theorem and applications.
4 Unit- IV
Univariate probability distributions: Discrete random variable,
probability mass function (pmf), cumulative distribution function
(cdf), properties of c.d.f., and examples. Definition of expectation
of random variable, properties of expectation, expectation of
function of random variable, definition of mean and variance of
univariate distribution.
Definitions of discrete uniform distribution, Bernoulli distribution,
Binomial distribution Poisson distribution, exponential
distribution and Normal distribution. Mean and variance of these
distributions, Important properties of these distributions.
Applications of these distributions.
13
Reference Books –
1. Bhat B. R., Srivenkatramana T. and Madhava Rao K. S. (1996): Statistics: A Beginner’s
Text, Vol. 1, New Age International (P) Ltd.
2. Edward P. J., Ford J. S. and Lin (1974): Probability for Statistical Decision Making,
Prentice Hall.
3. Goon A.M., Gupta M.K., and Dasgupta B.: Fundamentals of Statistics Vol. I and II, World
Press, Calcutta.
4. Hogg R. V. and Crag R. G.: Introduction to Mathematical Statistics Ed.4.
5. Hoel P. G. (1971): Introduction to Mathematical Statistics, Asia Publishing House.
6. Meyer P. L. (1970): Introductory Probability and Statistical Applications, Addision
Wesley.
7. Mood A. m., Graybill F. A. and Boes D. C. (1974): Introduction to the Theory Of Statistics,
McGraw Hill.
8. Rohatgi V. K. and Saleh A. K. Md. E. (2002): An Introduction to probability and statistics.
John wiley & Sons (Asia)
9. Snedecor G.W. and Cochran W. G. (1967): Statistical Methods, Lowa State University
Press.
10. Waiker and Lev.: Elementary Statistical Methods.