Probability, Statistics & Queuing Theory

Probability: Definitions of probability, Addition theorem, Conditional probability,
Multiplication theorem, Bayes theorem of probability and Geometric probability.
Random variables and their properties, Discrete Random variable, Continuous Random
variable, Probability Distribution joint probability distributions their properties, Transformation
variables, Mathematical expectations, probability generating functions.
Probability Distributions / Discrete distributions: Binomial, Poisson Negative binominal
distributions and their properties. (Definition, mean, variance, moment generating function.,
Additive properties, fitting of the distribution.)
Continuous distributions: Uniform, Normal, exponential distributions and their roperties.
Curve fitting using Principle of Least Squares.
Multivariate Analysis: Correlation, correlation coefficient, Rank correlation, Regression
Analysis, Multiple Regression, Attributes, coefficient of Association, χ2 – test for goodness of
fit, test for independence.
Sample, populations, statistic, parameter, Sampling distribution, standard error,
unbiasedness, efficiency, Maximum likelihood estimator, notion & interval estimation.
Testing of Hypothesis: Formulation of Null hypothesis, critical region, level of
significance, power of the test.
Small Sample Tests: Testing equality of .means, testing equality of variances, test of
correlation coefficient, test for Regression Coefficient.
Large Sample tests: Tests based on normal distribution
Queuing theory: Queue description, characteristics of a queuing model, study state
solutions of M/M/1: α Model, M/M/1 ; N Model.