Introduction

Elementary Concepts, Laws of Probability, Conditional probability And Bay’s theorem, Random variables.

Distribution of Sampling Statistics

Sample, Population, Sample mean & variance, Distribution of Sample mean, Markov inequality, Chebyshev’s inequality, Central Limit theorem.

Correlation and Analysis of Variance

Correlations, Rank correlation, One-way

analysis of variance, and Two factor analysis of variance

Parameter estimation and hypothesis testing.

Regression

Simple linear regression model, Estimation of the regression parameters, Method of least squares, Error of random variable, Regression to the mean, Coefficient of determination, Sample correlation coefficient hypothesis testing, Tests of independence and goodness of fit.

Parameter Estimation

Estimation of population mean, Interval estimators & lower- upper bounds of population mean using known and unknown variance.

Hypothesis Testing

Test concerning the mean of a normal population, Testing Equality of Means of Two Normal Populations, Test concerning the variance of normal population, Statistical significance, T-Tests, Chi-Square Tests, Chi-Square Test of goodness-of-fit.

Markov Chains

Discrete Time Markov Chains, Continuous Time Markov Chains, Birth-Death Process, Embedded Markov Chain.

Queuing Models

M/M/1, M/M/C, M/G/1, M/D/1, G/M/1, Open and Closed Queuing Network, Network of exponential servers, Phase-dependent arrival and Service application of queuing models.
Applied Statistics and Queuing Theory