UNIT I - PROBABILITY AND RANDOM VARIABLES
Axioms of probability – Conditional probability – Baye’s theorem - Discrete and continuous random variables – Moments – Moment generating functions – Binomial, Poisson, Geometric, Uniform, Exponential and Normal distributions – Functions of a random variable
UNIT II - TWO- DIMENSIONAL RANDOM VARIABLES
Joint distributions – Marginal and conditional distributions – Covariance – Correlation and linear regression – Transformation of random variables – Central limit theorem (for independent and identically distributed random variables)
UNIT III - ESTIMATION THEORY
Unbiased estimators - Efficiency - Consistency - Sufficiency - Robustness - Method of moments - Method of maximum Likelihood - Interval estimation of Means - Differences between means, variations and ratio of two variances
UNIT IV - NON- PARAMETRIC TESTS
Introduction - The Sign test - The Signed - Rank test - Rank - sum tests - The U test - The H test - Tests based on Runs - Test of randomness - The Kolmogorov Tests
UNIT V - STATISTICAL QUALITY CONTROL
Control charts for measurements ( 𝑋̅ and R charts ) – Control charts for attributes ( p, c and np charts) – Tolerance limits - Acceptance sampling