Probability & Statistics Syllabus - BCA (TU)

Course Description

This course covers basic concept of statistics.. measurement of central tendency, correlation & regression analysis, probability. sample survey, sample survey  methods and design of experiment. These topics are essential tools for research.

Course Objective

The general objectives of this course are to provide fundamental concept of Statistics, Probability, Sample Survey and their applications in the area of Social Science and Computer Application.

1. Introduction to Statistics  : 3 hrs

Meaning, Scope and Limitations of Statistics, Types and Sources of Data, Methods and Problems of Collection of Primary and Secondary Data. 

2. Descriptive Statistics : 6 hrs

Measure of Central Tendency (Arithmetic Mean, Median, Partition Values, Mode); Measure of Dispersion(Absolute and Relative Measures Range, Quartile Deviation, Mean Deviation, Standard Deviation and Coefficient of Variation)

3. Correlation and Regression Analysis : 3 hrs

Correlation: Definition, Scatter diagram, Karl Pearson's coefficient of correlation, Numerical problems for determination of Correlation Coefficients.

Regression: Definition, Dependent and Independent Variables, Least Square nethod only, Numerical Problems. 

4. Probability : 8 hrs

Definition of Probability, Two basic Laws of Probability( without proof), Conditional Probability; Probability Distributions(Binomial, Poisson and Normal); simple numerical problems.

5. Sample Survey : 6 hrs

Concept of Population and Sample; Needs of Sampling; Censuses and Sample Survey; Basic Concept of Sampling; Organizational Aspect of Sample Survey; Questionaire Design: Sample Selection and Determination of Sample Size; Sampling and Non Sampling Errors.

6. Sample Survey Methods : 10 hrs

Types of Sampling: Simple Random Sampling with and without Replacement; Stratified Random Sampling; Ratio and Regression Method of Estimation under Simple and Stratified Random Sampling; Systematic Sampling; Cluster Sampling;  Multistage Sampling; Probability Proportion to Size Sampling (PPS), Estimation of Population Total and its Variance, Sampling Distributions(t, x², z) and Related Problems.

7. Design of experiment : 6 hrs

Concept of Analysis of Variance(ANOVA), F-Statistic and its Distribution, Linear Model in ANOVA, Analysis of One Way, Two Way Classification(I and m observations per cell)in Fixed Effect Model.

Laboratory Works 

Techniques for using the computer as a tool in the analysis of statistical problems will be introduced. SPSS software should be used for data analysis

Text Books 

1. Mukhopadhyay P., “Theory and Methods of Survey Sampling”, Prentice Hall of India, New Delhi, 1998.
2. Sheldon M. Ross, “Introduction to Probability and Statistics for Engineers and Scientists”, 3^rd Edition, India, Acadernicilress, 2005

Reference Books 

1. Cochran W.G., “Sampling Techniques”, _^r eZif en, John Wiley -and Sons, Inc. New York, 1977.
2. Hogg & Tanis, “Probability and Statistical Inference”, 6¹¹¹ edition, First Indian Reprint, 2002