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# engineering statistics & linear algebra

Semester : IV

Course Code : 18EC44

CIE Marks : 40                       SEE Marks : 60

Module-1: Single Random Variables

Printed Notes

Module-2: Multiple Random variables

Printed Notes

Module-3: Random Processes

Printed Notes

Module-4: Vector Spaces

Handwritten Notes

Module-5: Determinants

Handwritten Notes

## ENGINEERING STATISTICS AND LINEAR ALGEBRA18EC44

### Module-1

Single Random Variables: Definition of random variables, cumulative distribution function continuous and discrete random variables; probability mass function, probability density functions and properties; Expectations, Characteristic functions, Functions of single Random Variables, Conditioned Random variables. Application exercises to Some special distributions: Uniform, Exponential, Laplace, Gaussian; Binomial, and Poisson distribution. (Chapter 4 Text 1)

### Module-2

Multiple Random variables: Concept, Two variable CDF and PDF, Two-Variable expectations (Correlation, orthogonality, Independent), Two variable transformations, Two Gaussian Random variables, Sum of two independent Random Variables, Sum of IID Random Variables – Central limit Theorem and law of large numbers, Conditional joint Probabilities, Application exercises to Chi-square RV, Student-t RV, Cauchy and Rayleigh RVs. (Chapter 5 Text 1)

### Module-3

Random Processes: Ensemble, PDF, Independence, Expectations, Stationarity, Correlation Functions (ACF, CCF, Addition, and Multiplication), Ergodic Random Processes, Power Spectral Densities (Wiener Khinchin, Addition and Multiplication of RPs, Cross spectral densities), Linear Systems (output Mean, Cross-correlation and Autocorrelation of Input and output), Exercises with Noise. (Chapter 6 Text 1)

### Module-4

Vector Spaces: Vector spaces and Null subspaces, Rank and Row reduced form, Independence, Basis and dimension, Dimensions of the four subspaces, Rank-Nullity Theorem, Linear Transformations
Orthogonality: Orthogonal Vectors and Subspaces, Projections and Least-squares, Orthogonal Bases and Gram- Schmidt Orthogonalization procedure. (Refer Chapters 2 and 3 Text 2)

### Module-5

Determinants: Properties of Determinants, Permutations and Cofactors. (Refer Chapter 4, Text 2) Eigenvalues and Eigen vectors: Review of Eigenvalues and Diagonalization of a Matrix, Special Matrices (Positive Definite, Symmetric) and their properties, Singular Value Decomposition. (Refer Chapter 5, Text 2)