Description
This course introduces the fundamental probability and statistical concepts used in basic data analysis. It will be taught at an introductory level to students who have completed junior or senior college-level mathematics, including calculus. A basic understanding of linear algebra and programming is helpful for the class, but it is not required.
In this course, you will learn :
- Statistics
- Confidence Interval
- Statistical Hypothesis Testing
- Biostatistics
Syllabus :
1. Introduction, Probability, Expectations, and Random Vectors
- Biostatistics and Experiments
- Set Notation and Probability
- Probability
- Random Variables
- PMFs and PDFs
- CDFs, Survival Functions, and Quantiles
- Expected Values
- Rules About Expected Values
- Variances and Chebyshev's Inequality
- Random Vectors and Independence
- Correlation
- Variance Properties and Sample Variance
2. Conditional Probability, Bayes' Rule, Likelihood, Distributions, and Asymptotics
- Conditional Probabilities and Densities
- Bayes' Rule and DLRs
- Likelihood
- Bernoulli Distribution and Binomial Trials
- The Normal Distribution
- Limits and LLN
- CLT and Confidence Intervals
2. Confidence Intervals, Bootstrapping, and Plotting
- Confidence Intervals and CI for Normal Variance
- Student's t Distribution and CI for Normal Means
- Profile Likelihoods
- T Confidence Intervals
- Plotting
- The Jackknife
- Bootstrapping
3. Binomial Proportions and Logs
- Binomial Proportions Part A
- Binomial Proportions Part B
- Logs