Download L T P/S SW/FW TOTAL CREDIT UNITS 3 1 4 0 6 Course Title

Course Title: Mathematical Statistics
Course Code:
Credit Units: 4
Level: PG
L
T
P/
S
SW/F
W
TOTAL
CREDIT
UNITS
3
1
4
0
6
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Course Title
1
Course Objectives:
The main objective of the course is to provide the detailed knowledge of
the random variable and its applications to various probability distributions.
Also illustrate the use of basic statistical tools to analyze the given data and
interpretation.
2
Prerequisites:
NILL
Student Learning Outcomes:
3

The students will be able to calculate moments, moment generating
function characteristic function, random variables and distribution
functions.

The students will learn to get the solution of the problems based on
probability distribution.

The students will learn to get the solution of the problems based
statistical inference.

4
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of 6
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The students will learn to get the solution of the problems based on
correlation and regression.
Course Contents / Syllabus:
Module I Random variable and mathematical expectation
20%
Weightage
Set of events. Operation on sets, sequences of sets and their limits, Random
variables and Distribution functions. Probability density function,
Probability mass function. Mathematical Expectation, Expectation of a
function of a random variable, conditional expectation, Moments of a
random variable, variance and covariance of a random variable. Moment
Generating function, Characteristic function, Probability generating
function.
5
Module II Probability distributions
30%
Weightage
Discrete distributions: Bernoulli, Binomial, Poisson, Geometric, Negative
Binomial, uniform, Hypergeometric and various properties. Computation
mean and variance through moment generating function. Fitting of
Binomial and Poission distribution.
Continuous distributions: Uniform, exponential, Gamma distribution,
Beta distribution, Normal distribution. Computation mean and variance
through moment generating function. Fitting of Normal distribution.
6
Module III Statistical Inference
35%
Weightage
Introduction to statistical inference, Population, sample, parameter,
Statistic and Estimator. Requirements of a good estimator: Unbiasedness,
Consistency, Sufficiency, C.R. inequality and efficiency. Examples based
on Normal, Binomial, Poisson, Geometric, Uniform, Exponential and
Gamma distributions.
Methods of Estimation: Method of Moments, Method of Maximum
Likelihood .Test of significance based on Normal distribution, Student tdistribution, Test of single mean, difference of two means, Paired t-test,
Chi-square, F-test and Analysis of variance (ANOVA) one way
classification.
7
8
Module IV Regression Analysis
15%
Weightage
Scatter diagram, Correlation, types of correlation, Spearman’s rank
correlation and properties of correlation. Linear Regression, lines of
regressions and regression coefficients. Introduction of Partial and Multiple
correlation and properties of residuals.
Pedagogy for Course Delivery:
1. All the topics covered in the syllabus will be correlated with its
applications in real life situations and also in other disciplines.
2. Extra sessions for revision will be undertaken.
11
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
End Term
Examination
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop
Mid-
70%
End Term
Examination
down)
Weightage
(%)
Term Assignments Viva Attendance
Exam
10%
7%
8%
5%
70%
Text & References:
1. Feller,W.(1971): Introduction to Probability Theory and its Applications, Vol. I and II. Wiley Eastern-Ltd.
2. V. K. Rohatgi, (1984): An Introduction to Probability Theory and Mathematical Statistics, Wiley Eastern.
3. Hogg, R.V. and Craig, A.T.(1971): Introduction to Mathematical Statistics, McMillan.
4. Mood, A.M., Graybill,F.A. and Boes, D.C.(1974): Introduction to the Theory of Statistics, McGraw Hill.
6. Gupta and Kapoor (2013): Fundamentals of Mathematical Statistics, Sultan Chand and Sons
Remarks and Suggestions:
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