Probability and Statistics

This course is a part of the AI Ascend program.
Probability and statistics form the foundation of data science.
This course will give the students a thorough understanding of probability theory, different kinds of probability distributions, testing hypotheses for mean and proportion, as well as dimensionality reduction.
A thorough experience with NumPy, SciPy, and scikit-learn packages is an additional strength of this course.
Job Roles-
- Data Scientist

At the end of this course, you should be able to:

Understand the concept of probability and its relation with mathematical sets
Be able to perform basic operations with sets and probabilities and use them to answer interesting questions
Contrast population and sample, parameter and its estimate
Understand and contrast the concepts of basic summary statistics, e.g., mean, variance, standard deviation, etc. for population versus samples and learn to estimate them from data
Understand the concept of effect size and uncertainty
Have a comprehensive idea about different kinds of probability distributions both discrete and continuous
Understand the concept of hypothesis, type I and II errors, level of significance, and power
Understand and be able to test hypotheses for mean and proportion and draw useful inferences from the process
Define and recognize the relation between covariance and Pearson’s correlation coefficient
Recognize the importance of dimensionality reduction, and comprehend principal component analysis. Along the way, you will learn about different matrix factorization techniques, eigenvalues, eigenvectors, their properties and interpretation

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At the end of this course, you should be able to:

Understand the concept of probability and its relation with mathematical sets
Be able to perform basic operations with sets and probabilities and use them to answer interesting questions
Contrast population and sample, parameter and its estimate
Understand and contrast the concepts of basic summary statistics, e.g., mean, variance, standard deviation, etc. for population versus samples and learn to estimate them from data
Understand the concept of effect size and uncertainty
Have a comprehensive idea about different kinds of probability distributions both discrete and continuous
Understand the concept of hypothesis, type I and II errors, level of significance, and power
Understand and be able to test hypotheses for mean and proportion and draw useful inferences from the process
Define and recognize the relation between covariance and Pearson’s correlation coefficient
Recognize the importance of dimensionality reduction, and comprehend principal component analysis. Along the way, you will learn about different matrix factorization techniques, eigenvalues, eigenvectors, their properties and interpretation

The idea of probability will be introduced starting from the concept of mathematical sets.
Students will learn how to perform basic probability operations and get an idea about conditional probability and Bayes’ theorem.
This will then be used to develop the idea about the different probability distributions, both discrete as well as continuous, using appropriate examples.
In between the concepts of different summary statistics such as mean, and variance will be introduced.
Students will also learn how to explore the pattern among multiple variables in the form of covariance, correlation, and principal component analysis.

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