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Subject

Probability and Statistics

Probability and Statistics introduces both foundational and advanced concepts essential for data analysis in the field of information and communication technology (ICT). Key topics include probability theory, random variables, probability distributions, statistical inference, hypothesis testing, confidence intervals, regression analysis, and applications of statistical methods in ICT. Students engage in lectures and practical sessions to apply these concepts, focusing on developing strong analytical and quantitative skills. Activities involve solving statistical problems, analyzing real-world data sets, utilizing statistical software tools, and collaborating on projects that require statistical modeling and interpretation. The course emphasizes best practices and explores current trends in statistical analysis and data-driven decision-making within the ICT industry.

Tribhuvan University

Faculty of Education

Course Title: Probability and Statistics

Course no: Math Ed. 436

Nature of course: Theory+Pratical

Full Marks: 100

Pass Marks: 40

Credit Hours: 3

Course Description : Probability and Statistics introduces both foundational and advanced concepts essential for data analysis in the field of information and communication technology (ICT). Key topics include probability theory, random variables, probability distributions, statistical inference, hypothesis testing, confidence intervals, regression analysis, and applications of statistical methods in ICT. Students engage in lectures and practical sessions to apply these concepts, focusing on developing strong analytical and quantitative skills. Activities involve solving statistical problems, analyzing real-world data sets, utilizing statistical software tools, and collaborating on projects that require statistical modeling and interpretation. The course emphasizes best practices and explores current trends in statistical analysis and data-driven decision-making within the ICT industry.

Course Objective : This module aims to impart the basic management knowledge, and skills to the students so as to enhance their managerial capabilities and enable them to apply in the practical field

Course Contents:
Unit 1. Unit I: Correlation 3 Hrs.

Types of correlation, Computation of correlation coefficient, Interpretation of r, Rank correlation, Properties of correlation.
Unit 2. Unit III: Probability Distribution 3 Hrs.

Sample space, events, Probability of an event, Axioms and theorems of probability, Conditional probability & Baye's theorem, Random variables, discrete random variable, probability function, probability distributions, cumulative distribution, Mathematical expectation, moments, mean and variance, Uniform distribution and its properties, Binomial distributions and its properties, Continuous random variable, probability density, cumulative density, mean and variance, Chebychev's inequality and laws of large numbers.
Unit 3. Unit II: Regression 3 Hrs.

Types of relationship, Estimation of regression equations, Properties of regression equations, Difference between correlation and regression.
Unit 4. Unit IV: Normal distributions 3 Hrs.

Meaning and Importance, Measure of Divergence from Normality, Properties: mean and variance, Area under the standard normal curves, Z score.
Unit 5. Unit VII Large Sample Test 3 Hrs.

Z-test: Difference between two means of large samples with unknown population variance
Unit 6. Unit V: Sampling Distribution and Estimation 3 Hrs.

Parameter and statistics, sampling distribution of mean/variance, Application of central limit theorem, Estimation: Point estimation, interval estimation, Confidence interval for mean and variance.
Unit 7. Unit VI: Test of Hypothesis 3 Hrs.

Null/alternate hypothesis, One/two tailed test, Type I and Type II errors, Level of significance, critical values, test statistics, Steps of hypothesis testing.
Unit 8. Unit VIII Small Sample Test 3 Hrs.

t-test: difference between two means of small samples with unknown common varianceChi-square test: significance of independence, r-test: Significance of test for correlation coefficient.
Reference Books: