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.

- Teacher: Kiran Patil