# GITAM University Probability and Statistics Syllabus

UNIT – I

Probability: definitions of Probability, addition theorem, conditional Probability, Multiplication theorem, Baye?s theorem of Probability and Geometric Probability. Random Variables and their properties, Discrete Random Variable, Continuous Random Variable, Probability Distribution, Transformation variables, Mathematical expectations , Probability generating functions, Probability distribution / Discrete distributions : Binomial , Poisson , negative binomial distributions and their properties.(Definition, mean, variance, moment generating function, additive properties , fitting of the distribution)

UNIT – II

Continuous distributions: Uniform, normal exponential distributions and their properties. rectangular distribution and its properties. Curve fitting – Principle of least squares, method of least squares, working procedure, Fitting of other curves.

UNIT – III

Multivariate Analysis: correlation, correlation coefficient, Rank correlation, Regression analysis, ?2 –test for goodness of fit, test for independence. Estimation : Sample, populations, statistic, parameter, sampling distribution, standard error, unbiasedness, efficiency, maximum likelihood estimator, notion & interval estimation

UNIT – IV

Testing of Hypothesis: Formulation of Null Hypothesis, critical regions, level of significance, power of the test.

UNIT – V

Small sample Tests: Testing equality of means, testing equality of variances, test of correlation coefficients, test for regression coefficient.

Large sample Tests: Tests based on Normal distribution.

Text Book:

1. Fundamentals of Mathematical Statistics – S.C. Gupta & V.K.Kapoor S.Chand Publications.

Reference books:

1) Probability Statistics with Reliability, Queuing and Computer Science Application –

Kishar . S, Trivedi, PHI Publicatioin.

2) Probability & Statistics – M.R. Spiegel, J.Schiller & R Alu Srinivasan – Schum Series –

McGrahill Publications.

UNIT – I

Probability: definitions of Probability, addition theorem, conditional Probability, Multiplication theorem, Baye?s theorem of Probability and Geometric Probability. Random Variables and their properties, Discrete Random Variable, Continuous Random Variable, Probability Distribution, Transformation variables, Mathematical expectations , Probability generating functions, Probability distribution / Discrete distributions : Binomial , Poisson , negative binomial distributions and their properties.(Definition, mean, variance, moment generating function, additive properties , fitting of the distribution)

UNIT – II

Continuous distributions: Uniform, normal exponential distributions and their properties. rectangular distribution and its properties. Curve fitting – Principle of least squares, method of least squares, working procedure, Fitting of other curves.

UNIT – III

Multivariate Analysis: correlation, correlation coefficient, Rank correlation, Regression analysis, ?2 –test for goodness of fit, test for independence. Estimation : Sample, populations, statistic, parameter, sampling distribution, standard error, unbiasedness, efficiency, maximum likelihood estimator, notion & interval estimation

UNIT – IV

Testing of Hypothesis: Formulation of Null Hypothesis, critical regions, level of significance, power of the test.

UNIT – V

Small sample Tests: Testing equality of means, testing equality of variances, test of correlation coefficients, test for regression coefficient.

Large sample Tests: Tests based on Normal distribution.

Text Book:

1. Fundamentals of Mathematical Statistics – S.C. Gupta & V.K.Kapoor S.Chand Publications.

Reference books:

1) Probability Statistics with Reliability, Queuing and Computer Science Application –

Kishar . S, Trivedi, PHI Publicatioin.

2) Probability & Statistics – M.R. Spiegel, J.Schiller & R Alu Srinivasan – Schum Series –

McGrahill Publications.