NOC- Probability and Statistics

Explore the fundamentals of probability and statistics through a comprehensive 21-hour course covering a wide range of topics. Delve into descriptive statistics, special continuous distributions, joint distributions, bivariate normal distribution, and transformation of random variables. Learn about chi-square, t, and F distributions, as well as estimation techniques like LSE, MME, and MLE. Master hypothesis testing concepts, including Neyman-Pearson Lemma, paired t-tests, and chi-square tests for goodness of fit and independence. Gain practical skills in analyzing contingency tables, testing for equality of proportions, and handling large sample tests for variance and mean. Apply these concepts through numerous examples and problem-solving exercises throughout the course.

Syllabus

Chi-Square Test for Goodness Fit - I.
Testing for Independence in rxc Contingency Table - II.
Applications of N-P-Lemma - I.
Testing Equality of Proportions.
Testing for Independence in rxc Contingency Table - I.
Neyman- Pearson Fundamental Lemma.
Examples.
Two Types of Errors.
Paired t-Test.
Testing for Normal Variance.
Large Sample Test for Variance and Two Sample Problem.
Testing for Normal Mean.
Chi-Square Test for Goodness Fit - II.
Examples on MLE - I.
Examples on MME, MLE.
LSE, MME.
Introduction to Estimation.
Descriptive Statistics - IV.
Descriptive Statistics - III.
Descriptive Statistics - II.
Descriptive Statistics - I.
F-Distribution.
Chi - Square Distribution (Contd.)., t-Distribution.
Chi - Square Distribution.
Transformation of Random Variables.
Additive Properties of Distributions - II.
Additive Properties of Distributions - I.
Bivariate Normal Distribution - II.
Bivariate Normal Distribution - I.
Linearity property of Correlation and Examples.
Independence , product moments.
Joint Distributions - II.
Joint Distributions - I.
Function of a random variable - II.
Function of a random variable - I.
Problems on special distributions - II.
Problems on special distributions - I.
Problems on normal distribution.
Special continuous distributions - IV.
Special continuous distributions - III.
Special continuous distributions - V.
Normal distribution.
Special continuous distributions - II.