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 ( ̅ and R charts ) – Control charts for attributes ( p, c and np charts) – Tolerance limits – Acceptance sampling. T