3 Review(s)

UNIT - I Probability : Sample Space, Events, Counting Sample Points, Probability of an Event, Additive Rules, Conditional Probability, Independence, and the Product Rule, Bayes’ Rule. Random Variables and Probability Distributions : Concept of a Random Variable, Discrete Probability Distributions, Continuous Probability Distributions, Statistical Independence. (Chapter - 1) UNIT - II Mathematical Expectation : Mean of a Random Variable, Variance and Covariance of Random Variables, Means and Variances of Linear Combinations of Random Variables, Chebyshev’s Theorem. Discrete Probability Distributions : Introduction and Motivation, Binomial Distribution, Geometric Distributions and Poisson distribution. (Chapter - 2) UNIT - III Continuous Probability Distributions : Continuous Uniform Distribution, Normal Distribution, Areas under the Normal Curve, Applications of the Normal Distribution, Normal Approximation to the Binomial, Gamma and Exponential Distributions. Fundamental Sampling Distributions : Random Sampling, Some Important Statistics, Sampling Distributions, Sampling Distribution of Means and the Central Limit Theorem, Sampling Distribution of S2, t –Distribution, F-Distribution. (Chapter - 3) UNIT - IV Estimation & Tests of Hypotheses : Introduction, Statistical Inference, Classical Methods of Estimation.: Estimating the Mean, Standard Error of a Point Estimate, Prediction Intervals, Tolerance Limits, Estimating the Variance, Estimating a Proportion for single mean, Difference between Two Means, between Two Proportions for Two Samples and Maximum Likelihood Estimation. Statistical Hypotheses : General Concepts, Testing a Statistical Hypothesis, Tests Concerning a Single Mean, Tests on Two Means, Test on a Single Proportion, Two Samples : Tests on Two Proportions. (Chapter - 4) UNIT - V Stochastic Processes and Markov Chains : Introduction to Stochastic processes - Markov process. Transition Probability, Transition Probability Matrix, First order and Higher order Markov process, n step transition probabilities, Markov chain, Steady state condition, Markov analysis. (Chapter - 5)