Since Data science and Machine learning rule the world we need to know what are the basic things that make these concepts works. For learning making the most out of machine learning and datascience it is crucial for us to learn probability and statistics inorder to get the deeper understanding of the concepts in machine learning and data science. In the following posts you are introduced and taken deeper into the probability concepts and how it closely related to statistics.

The prerequisite for learning this topic is

- Differential calculus \lim_{x\to\infty} f(x)
- Integral calculus \int_{-\infty}^{\infty} f(x)dx

This post is written in LaTeX and WordPress.

Let us see what are the topics covered

- Basic Probability
- Discrete Random Variables
- Continuous random variables

Basic Probability

The topics that are covered under basic probability are

- Set Notation eg. Universal Set : \Omega
- Probability Axioms eg . P(A) \geq 1
- Counting eg . n_1 \times n_2 \times n_3 \times n_4 \times ... \times n_k
- Conditional Probability P(A | B) = \frac{P(A \cap B)}{P(B)} Provided P(B) > 0
- Law of Total Probability P(A) = \sum_{i=1}^{n}P(A|B_i)P(B_i)
- Bayes rule P(B_j|A)=\frac{P(A\cap B_j)}{P(A)}=\frac{P(A|B_j)P(B_j)}{P(A)} for j=1,....,n

Discrete Random Variables

The topics that are covered under Discrete Random Variables are

- Probability Mass function \sum_{y_i \in \Omega_Y} f_Y(y_i) = 1
- Expected Values E[Y] = \sum_{y_i \in \Omega_y} y_i f(y_i)
- Variance Var(Y) = E[Y^2] - (E[Y])^2
- Standard Deviation \sqrt{Var(Y)}
- Geometric Distribution f(y) = (1-p)^{y-1} p, y=1,2,...
- Binomial Distribution f(y) = \binom ny p^y(1-p)^{n-y}, y=0,1,2,....,n
- Poisson Distribution \frac{e^{-\lambda}\lambda^y}{y!}

Continuous Random Variables

The topics that are covered under Continuous Random Variables are

- Probability Density function F(y)=\int_{-\infty}^{y} f(t)dt
- Expected Values E[Y] = \int_{-\infty}^{\infty} y f(y) dy
- Variance Var(Y) = E[(Y - \mu)^2]
- Uniform Distribution f(n) = \begin{cases} \frac{1}{b-a} , & \quad a \leq y \leq b, \\ 0, & \quad elsewhere. \end{cases}
- Normal Distribution f(y) = \frac{1}{\sigma \sqrt {2\pi}}e^{-\frac{(y-\mu)^2}{2\sigma^2}}, -\infty < y < \infty
- Exponential Distribution f(y) = \begin{cases}\lambda e^{-\lambda y} , & \quad 0 \leq y \leq \infty, \lambda > 0 \\ 0, & \quad otherwise \end{cases}

We will see all these topics in detail in the next posts.

Happy Learning

Thank You