Data Science Foundations: Statistical Inference

Module 1: Probability Theory: Foundation for Data Science

• Explain the importance of probability in statistics and data science.
• Explore the relationship between conditional and independent events in a statistical experiment.
• Calculate the expectation and variance of random variables and develop intuition in probability theory.

Module 2: Statistical Inference for Estimation in Data Science

• Identify characteristics of "good" estimators and compare competing estimators.
• Construct sound estimators using maximum likelihood and method of moments estimation techniques.
• Construct and interpret confidence intervals for one and two population means, proportions, and a population variance.

Module 3: Statistical Inference and Hypothesis Testing in Data Science Applications

• Define a composite hypothesis and the level of significance for a test with a composite null hypothesis.
• Define a test statistic, level of significance, and the rejection region for a hypothesis test.
• Perform tests concerning a true population variance and compute the sampling distributions for the sample mean and sample minimum of the exponential distribution.