To understand the concept of sampling and sampling distributions and its applications.
Concept of statistic and sampling distribution. Sampling Distribution of sum of Binomial, Poisson and mean of Normal Distribution. Standard Error: Meaning and role. The Central Limit Theorem for identically independently distributed (i.i.d) random variable. Hypothesis and its procedure of testing.
Definition, Derivation, Moments, Moment Generating Function, Cumulant Generating Function. Limiting and Additive property of Chi-square variates. Distribution of ratio of chi-square variates
Chi-square test for testing normal population variance, Test for goodness of fit, Contingency table and Test for independence of attributes, Yates correction for 2x2 contingency table conditions of Chi-square.
Definition of Student’s-t and Fisher’s-t statistics and derivation of their distributions. Limiting property of t-distribution. Applications: Testing of single mean, Difference of two means, paired t-test and test of sample correlation coefficient.
Definition of Snedecor’s F-distribution and its derivation. Applications- Testing of equality of two variance. Fisher’s transformation and its uses. Relationship between‘t’, ‘F’ and chi-square statistics.
1. Goon, A.M., Gupta, M.K. and Dasgupta, B. (1991): Fundamentals of Statistics,
Volume II, The World Press Pvt Ltd, Calcutta
2. Gupta, S.C. and Kapoor, V.K.: Fundamentals of Mathematical Statistics, S Chand &
Company, New Delhi
1. Mood Alexander M., Graybill Frankline and Boes Duane C.: Introduction to Theory of Statistics, Mc Graw Hill & Company Third Edition
2. Speigel M.R., (1967): Theory and Problem of Statistics, Schaum’s Publishing Series.
3. Gupta, O.P.:Mathematical Statistics, Kedarnath Publication, Meerut
4. Goon, A.M., Gupta, M.K. and Dasgupta, B. (1991): An Outline of Statistics Volume
II,The World Press Pvt Ltd, Calcutta
Links:
[1] https://www.statistics.iisuniv.ac.in/courses/subjects/sampling-distributions-5
[2] https://www.statistics.iisuniv.ac.in/academic-year/2014-2015