Verify Account

SYLLABUS

UNIT-I

Basic Probability Probability Spaces, Conditional Probability, Independent Events and Bayes’ Theorem. Random Variables: Discrete and Continuous Random Variables, Expectation of Random Variables, Moments, Variance of Random Variables.

UNIT-II

Probability Distributions Binomial, Poisson, Evaluation of Statistical Parameters for These Distributions, Poisson Approximation to the Binomial Distribution. Continuous Random Variables and Their Properties, Distribution Functions and Density Functions, Normal and Exponential, Evaluation of Statistical Parameters for These Distributions.

UNIT-III

Testing of Hypothesis Test of Significance: Basic of Testing of Hypothesis. Null and Alternate Hypothesis, Types of Errors, Level of Significance, Critical Region. Large Sample Test for Single Proportions, Difference of Proportions, Single Mean, Difference of Means, Small Sample Tests: Test for Single Mean, Difference of Means and Test for Ratio of Variances.

UNIT-IV

Complex Variables (Differentiation) Limit, Continuity and Differentiation of Complex Functions, Analyticity, Cauchy-Riemann Equations (without proof), Finding Harmonic Conjugate; Elementary Analytic Functions (Exponential, Trigonometric, Logarithm) and Their Properties.

UNIT-V

Complex Variables (Integration) Line Integral, Cauchy’s Theorem, Cauchy’s Integral Formula, Zeros of Analytic Functions, Singularities, Taylor’s Series, Laurent’s Series; Residues, Cauchy Residue Theorem, Conformal Mappings, Mobius Transformations and Their Properties.