A courseware module that covers the fundamental concepts in probability theory and their implications in data science. Topics include probability, random variables, and Bayes' Theorem.

On a certain track team, the runners all take between 4 and 7 minutes to finish a mile. The probability density function for the length of time it takes a runner to ...

What does the protein content in cows' milk have in common with human IQ? Both variables have approximately normal distributions. The normal distribution is a good model for measurements of many kinds ...

A discrete random variable is a type of random variable that can take on a countable set of distinct values. Common examples include the number of children in a family, the outcome of rolling a die, ...

The total area under the curve must equal 1, representing the fact that the probability of some outcome occurring within the entire range is certain. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

Roll a die and ask students to identify the random variable. Since a die can only take on values of 1, 2, 3, 4, 5, or 6, this is a discrete random variable. Repeat ...

Test of independence is a fundamental problem in statistics, with many existing work including the maximal information coefficient (MIC) [1], the copula based measures [2,3], the kernel based ...