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UNIT I RANDOM VARIABLES Discrete and continuous random variables – Moments – Moment generating functions – Binomial, Poisson, Geometric, Uniform, Exponential, Gamma and Normal distributions. UNIT II TWO - DIMENSIONAL RANDOM VARIABLES Joint distributions – Marginal and conditional distributions – Covariance – Correlation and Linear regression – Transformation of random variables. UNIT III RANDOM PROCESSES Classification – Stationary process – Markov process - Poisson process – Discrete parameter Markov chain – Chapman Kolmogorov equations – Limiting distributions. UNIT IV QUEUEING MODELS Markovian queues – Birth and Death processes – Single and multiple server queueing models – Little’s formula - Queues with finite waiting rooms – Queues with impatient customers: Balking and reneging.