Day 01 with Datascience

 Mathematics and Data science

Probability 

Probability topics required for Data Science

Core probability (very important)

• Definition of probability

• Sample space and events

• Conditional probability

• Bayes’ Theorem

• Independent and dependent events

• Law of Total Probability

Random variables

• Discrete random variables

• Continuous random variables

• Probability Mass Function (PMF)

• Probability Density Function (PDF)

• Cumulative Distribution Function (CDF)

• Expected value (mean)

• Variance and standard deviation

Probability distributions

Discrete distributions

• Bernoulli distribution

• Binomial distribution

• Poisson distribution

• Geometric distribution

Continuous distributions

• Uniform distribution

• Normal (Gaussian) distribution

• Exponential distribution

• Gamma distribution

Sampling and limit theorems

• Random sampling

• Sampling distributions

• Law of Large Numbers

• Central Limit Theorem

Bayesian probability

• Prior probability

• Likelihood

• Posterior probability

• Bayesian inference

• Maximum Likelihood Estimation (MLE)

• Maximum A Posteriori (MAP)

• Naive Bayes classifier

Statistics linked with probability

• Descriptive statistics

• Hypothesis testing

• Confidence intervals

• p-values

• Type I and Type II errors

Probability used in machine learning

• Logistic regression

• Naive Bayes

• Hidden Markov Models

• Recommendation systems

• A/B testing

Learning order (recommended)

1. Basic probability rules

2. Random variables and distributions

3. Bayes theorem

4. Sampling and Central Limit Theorem

5. Hypothesis testing

6. Bayesian methods