I. Probability models - axioms of probability - addition and Multiplication rules of probability - conditional probability and Bayes theorem. Discrete and Continuous random variables - Probability mass function, probability density function - Cummulative distribution functions - Mathmatical exception - moment generating function - Binomial distribution Moments of these distributions. Uniform, normal exponential, Beta, Gamma distributions - Concept of sample, standard error, sampling distribution - T ,f and x^2 distributions.

II. Statistical inference - Statements of weak law of large numbers and The central limit theorem - Estimation of parameters - unbiassedness, efficiency and consistency - methods of moments- method of maximum likelihood - internal estimation - confidence limits.

Testing of hypotheses - Tests as populations means(s) -
Hypotheses concerning variences - fooness of fit test - Test bases On t and f distributions.

III. Mrkov chains - Computation of n-step transition probabilities State classification and limiting distributions - Continuous Parameter Markov chains - possion process - the birth and death process.

Queues Characteristics of queue m/m/1 queue - steady state probablities M/G/1 queuing systems

Reliability concept of reliability, failure density and hazard function - system reliability- series Parallel and k-out of n systems - computation of mean time to failure

IV Linear programming (LP) - Construction of LP model - Graphical LP solution - Graphical sensitivity analysis - The simplex Method - Standard LP form and its basic solutions - the simplex Algorithm - Artificial starting solutions - special cases in simplex Method application -Definition of dual problem - Economic inter - pretation of duality - Dual simplex method.

Text Book
1. Kisor S. Trivedi Probability and Statistics with reliability, queueing and Computer Science Applications Prentice Hall of India, New Delhi (1998)
2. Hogg and Craig : Introduction to Mathematical Statistics
3. Hamdy A. Taha, operations Research, and introduction (Smith Edition) Prentice Hall of India, New Delhi (1998)