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.

Defination, simple and composite hypothesis. Null and alternative hypothesis, procedure of testing, two types of error, critical region level of significance, critical and p-values, statistical test: one tailed and two tailed test, power and size of the test.

Definition, Derivation, Moments, Moment Generating Function, Cumulant Generating Function. Limiting and Additive property of Chi-square variates. Distribution of ratio of chi-square variates.Applications of Chi-square: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 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.