Download Course Title: Statistical Methods and Probability Distribution

Annexure ‘CD – 01’
Course Title: Statistical Methods and Probability Distribution
Course Code: MSA 102
Credit Units: 03
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Course Title
Course Objectives: To familiarize students with the basic procedures for summarization,
analysis and presentation of statistical data and also introduce probability concepts,
characteristics of the basic univariate distribution, joint and conditional distribution,
correlation, regression and statistical software SPSS.
Pre-requisites: Student should have basic knowledge of probability, statistics and
calculus.
Student Learning Outcomes:
On completion the student will be able to:
(1) Summarize the main features of a data set.
(2) Explain and apply concepts of probability, conditional probability and independence
of events.
(3) Specify the meaning and application of a probability distribution and the distribution
function of a random variable, the expected value of a random variable and the
expectation of functions of a random variable for both a discrete and continuous random
variable.
(4) Recognize and evaluate features of some basic standard discrete and continuous
distribution and their features.
(5) Generate values of a random variable from a specified distribution using simulation
methods.
(6) Write and make use of joint distribution and marginal and conditional distribution,
distribution of one or more linear combinations of several random variables.
TOTAL
CREDIT UNITS
03
Comments (if any)
(7) Describe and explain the meaning of co-variation and evaluate strength of correlation
between variables, Use of least square regression models, evaluate coefficient of
determination, Describe/explain multiple linear regression, multiple and partial
correlation.
Course Contents/Syllabus:
Module I: Data Collection, Presentation and Summarization
Data type
Primary vs. secondary
Qualitative (attributive) vs. quantitative; nominal, ordinal, interval and ratio measurement
scales
Presentation of Data
:
Tabulation-Frequency Distribution, Frequency
Tables
Cumulative
Frequency
Distribution
Graphical Methods and
:
Charts Histogram and cumulative frequency curves
Diagrammatic presentation
(ogives) Stem-leaf and Box-plot, Graphical
presentation of time
series data
Measures of Location
:
Mean, median and mode, quartiles
Measures of Spread
:
Range, Semi-inter quartile range, mean deviation,
standard deviation, coefficient of variation
Measures of Skewness
:
Symmetry and skewness, kurtosis; measures based
on moments
and other measures.
Module II: Probability Concepts
Basic elements of probability: sample space, simple events, mutually exclusive events,
addition rule of probability, conditional probability definition, independence of events,
multiplication rule of probability, law of total probability, Bayes’ theorem.
Module III: Random Variables, Expectation & Generating Functions
Random variables Distributions of random variables and their probability functions.
Probability mass function (pmf) and cumulative distribution function (cdf) for a discrete
random variable.
Probability density function (pdf) and cumulative distribution function (cdf) for a
continuous random variable; Expected value of a random variable.
Comments (if any)
5% Weightage
10% Weightage
20% Weightage
Expected value of a function of a random variable;
Properties of an expected value, variance and moments of the distribution of a random
variable; factorial moment of discrete random variables.
Generating functions: Probability generating function for a discrete random variable,
factorial – moment generating function, moment generating function and cumulant
generating function for a random variable.
Markov inequality and Chebychev Inequality
Module IV: Univariate Distributions
Discrete distributions: Uniform, Bernoulli, Binomial, Geometric, Negative binomial,
Hyper geometric, Poisson (with Poisson process postulates); other discrete distributions
(beta-binomial and logarithmic); truncated and censored random variables.
Continuous distributions: Uniform (Rectangular), Normal, Exponential, Gamma, Beta;
Lognormal, Pareto, Weibull, Burr, Laplace (double- exponential); truncated distributions
Module V: Joint Distributions & Conditional Distributions
Jointly distributed discrete and continuous random variables, joint probability (mass and
density) functions, Joint cumulative distribution function (bivariate case) marginal
distributions, Marginal density function, marginal pmf, Marginal pdf, marginal cdf,
Multinomial distribution, bivariate normal distribution, Conditional distributions,
conditional pmf, conditional pdf, conditional cdf.
Stochastic independence of random variable-discrete and continuous case; random
variables uncorrelated .Expectation of uncorrelated functions of jointly distributed
random variables, covariance and correlation coefficient.
Conditional expectation and conditional variance. Expectation of product of functions of
independent random variables, Joint moment generating functions and moments;
Properties for expectation, moments and mgf.
Module VI: Correlation and Regression
Correlation: Simple, partial and multiple correlation measures.
Linear regression models, Response Variable and Covariates, Linear prediction of
response variable, least squares fitting method, residuals; Partition of variation of
response variable into “explained” and “unexplained” parts, coefficient of determination;
multiple linear regression model and its fitting; examination of residuals and model
diagnostics; step-up regression method.
Module VII: Simulation
20% Weightage
20% Weightage
10% Weightage
5% Weightage
General techniques for simulating continuous random variables
 The Inverse transformation Method
 The Rejection Method
 The Hazard Rate Method
Special techniques for simulating continuous random variables.
1. Normal distribution, Gamma distribution, Chi –Square distribution,
a. Variance Reduction techniques
1. Use of Antithetic Variables
2. Variance of Reduction by conditional Monte Carlo
3. Control Variates
4. Importance sampling
Module VIII: Computer application of probability distribution using SPSS
Managing Data: Listing cases, replacing missing values, computing new variables,
recording variables, exploring data, selecting cases, sorting cases, merging files, Listing
data
Graphs: Creating and editing graphs and charts
Frequencies: Frequencies, bar charts, histograms, percentiles
Descriptive Statistics: measures of central tendency, variability, deviation from
normality, size and
stability. Cross Tabulation and chi-square analyses
The means Procedure
Bivariate Correlation: Bivariate Correlation, Partial Correlations and the correlation
matrix
Regression: Simple Linear Regression, Multiple regression analysis
10% Weightage
Pedagogy for Course Delivery:
 Lectures
 Assignments
 Practicals
Assessment/ Examination Scheme:
Theory L/T (%)
100%
Lab/Practical/Studio (%)
End Term Examination
100%
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components (Drop down)
End Term
Examination
Class Test
Assignment
Practical
Attendance
10%
5%
10%
5%
Weightage (%)
30%
Text & References:
 John E Freund’s Mathematical Statistics with Applications: Irwin Miller and Marylees Miller, Pearson Education
 Modern Mathematical statistics: E.J. Dudewicz and S.N. Mishra,Wiley
 Business Statistics:J.K.Sharma, Pearson Education
Remarks and Suggestions:
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Date:
Name, Designation, Organisation