Measures Of Central Tendency:
Introduction, Arithmetic Mean, Simple and weighted for raw data, Discrete frequency distribution, Continuous frequency distribution, Properties of A.M., Merits & De merits of A.M., Median for raw data, Discrete frequency distribution, Continuous frequency distribution, Merits and demerits of Median, Mode for raw data, Merits & demerits of mode.
Measures Of Dispersion:
Introduction, Range, coefficient of range, Quartiles, Quartiles deviations, coefficient of quartile deviations, Mean deviation and coefficient of mean deviation, S.D and variance for all types of frequency distribution, Coefficient of Dispersion, Coefficient of variation.
Definition of Correlation, Types of Correlation, Scatter Diagram Method, Karl Person’s Correlation Coefficients, Correlation Coefficients for Bivariate frequency distribution, Probable error for Correlation Coefficients, Rank Correlation Co-efficient.Definition of Regression, Regression lines, Regression Coefficients
Introduction, Random Experiment, Sample Space, Events, Complementary Events, Union and Intersection of Two Events, Difference Events, Exhaustive Events, Mutually Exclusive Events, Equally Likely Events, Independent Events, Mathematical & Statistical definition of Probability, Axiomatic definition of probability, Addition Theorem, Multiplication Theorem, Theorems of Probability, Conditional Probability, Inverse Probability.
Introduction, Probability mass function of Binomial distribution, Mean and Variance of Binomial distribution, Properties of Binomial Distribution, Uses of Binomial Distribution.
Introduction, Probability mass function of Poisson distribution, Mean and Variance of Poisson distribution, Properties of Poisson Distribution, Applications of Poisson Distribution.
Introduction, Probability density function of Normal distribution, Properties of Normal distribution, Importance of Normal Distribution.
Types of Error, Power of a test, Goodness of a fit, Student t and Chi square; Sufficient Statistic and MLEs; Limit theorems and convergence of random variables; Elementary concepts related to stochastic processes; Forecasting and Modelling applications.
Random (Stochastic) processes (RP)
Introduction and Definition, continuous and discrete time process, moments of RP, autocorrelation, independence and uncorrelated process, Independent and Identically Distributed Process, its moments: mean, variance, covariance,Wiener process, strict sense stationary (SSS), Wide-sense stationary process (WSS) their mean, variance, autocorrelation function, continuity (mean square) of RP, Time average of RP, mean and variance of time averages, Ergodicity principle, white noise process, band limitation in white noise, Linear systems and signal estimation in presence of noise