Mathematics 3 Notes

## 1. Probability

- Axiomatic approach to probability theory

- Univariate probability distributions (discrete and continuous)

- Standard distributions:

- Binomial

- Poisson

- Geometric (?)

- Exponential

- Normal

- Uniform

- Gamma (?)

- Bivariate distributions:

- Concepts of joint and conditional distributions

- Mathematical concepts:

- Expectation, variance, and covariance

- Correlation coefficient

- Tchebycheff’s inequality

## 2. Statistics

- Concept of Statistics

- Sample correlation coefficients

- Curve fitting:

- Method of Least Squares

- Simple Regression models

## 3. Laplace Transform

- Definition

- Laplace transform of elementary functions

- Basic operational properties

- Inverse Laplace transform

- Convolution theorem

- Applications:

- Initial value problems involving Ordinary Differential Equations