Probability and Statistics

Birla Institute Of Technology And Science–Pilani (BITS–Pilani) via Coursera

Go to class Write review

Overview

Coursera Flash Sale

40% Off Coursera Plus for 3 Months!

Grab it

Elevate your data analysis skills with our comprehensive Probability and Statistics course, tailored for professionals seeking real-world applications. Ideal for aspiring data analysts, engineers, scientists, and anyone looking to enhance their decision-making abilities, this course is your gateway to mastering essential statistical concepts. Dive deep into data sets, Chebyshev’s inequality, descriptive statistics, probability axioms, and Bayes’ formula. Gain expertise in random variables, mathematical expectations, various distributions, confidence intervals, hypothesis testing, and regression analysis. Our interactive course features discussions and ample assignments designed to solidify your understanding and competencies. Real-world applications are seamlessly integrated, ensuring you can apply concepts in practical scenarios. Whether you're aiming for a career in data science, engineering, finance, or research, this course equips you with critical analytical skills to succeed and stand out in your field. Enrol now to transform your ability to make data-driven decisions with confidence. With our expert-driven learning experience, enhance your career and become a valuable asset in your professional journey. Keywords: Probability and Statistics course, data analysis, real-world applications, aspiring data analysts, decision-making, career enhancement.

Syllabus

Fundamentals of Statistics

In this module, you will be introduced to statistics and descriptive statistics. You will learn about various visualizations to understand the data. You will understand various measures of central tendency and measures of variability to analyze the given data for more insights.

Elements of Probability

In this module, you will be introduced to the basics of set theory and probability. You will learn about the axioms of probability and conditional probability. You will understand the difference between dependent and independent events. You will also explore one of the important concepts in data science (machine learning), i.e., Bayes’ formula.

Random Variables

In this module, you will learn how to generalize the events and their outcomes by a variable, that is, a random variable. You will explore types of random variables. You will gain an understanding of a mathematical expectation. You will further learn about the procedure to find the mean and variance using mathematical expectation. This module also covers the probability distribution function.

Discrete Probability Distributions

In this module, you will learn about various discrete probability distributions. You will be able to understand Binomial and probability distributions with their corresponding probability distribution functions. You will also learn about the mean and variance of Binomial and Poisson distributions.

Continuous Probability Distributions

In this module, you will learn continuous probability distributions in general and normal/Gaussian distribution in particular. You will gain an understanding of the mean and variance of normal distribution. You will also explore the standard normal distribution with the help of normal distribution tables. Furthermore, you will be introduced to other continuous distributions like uniform distribution and Gamma distribution.

Sampling and Estimation

In this module, you will learn the importance of sampling and various sampling techniques. You will be introduced to sampling distribution, which plays an important role in understanding data. You will learn about the central limit theorem that will help you understand the use of normal distribution in many situations. Then, you will be introduced to the next step in sampling, that is, estimation. You will also gain an understanding of the t- and chi-square distribution.

Testing of Hypothesis

In this module, you will learn to identify and validate hypotheses using various statistical techniques, including sampling. You'll cover forming hypotheses, type I and type II errors, and their impact on test significance and power. The module also explores hypothesis testing with proportions, handling both large and small samples, and validating multiple proportions using the chi-square test.

Correlation and Regression

In this module, you will learn how to understand the relation between two variables in the given data and the types of correlation that exists between two variables. You will be able to find coefficient correlation to establish this. The module answers why it is important to use the given data for future prediction for which regression is helpful. This module will also help you understand simple linear regression with the help of normal equations and their matrix form.

Multiple Linear Regression and Nonlinear Regression

In this module, you will learn how to predict when nonlinearity exists in the data. With the learnings from simple linear regression, you will understand the regression for prediction when nonlinearity exists in the data. Furthermore, in nonlinear regression, you will focus on polynomial regression.