Abstract: We show that the entropy of the sum of independent random variables can greatly differ from the entropy of their difference. The gap between the two entropies can be arbitrarily large. This ...

A variable is a factor in an experiment that can be changed. When you set up an experiment in the correct way you need to think about control, independent and dependent variables. What is an ...

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.

Abstract: In this chapter, we introduce the concept of a random variable and develop the procedures for characterizing random variables, including the cumulative distribution function, as well as the ...

Will Kenton is an expert on the economy and investing laws and regulations. He previously held senior editorial roles at Investopedia and Kapitall Wire and holds a MA in Economics from The New School ...

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 ...

In a raffle with 20 tickets, 6 tickets are drawn for prizes. The first prize winner gets $\$20$, 2 second prize winners get $\$10$, and three third prize winners get $\$5$. What is the sample space ...

The FactorGraph package provides the set of different functions to perform inference over the factor graph with continuous or discrete random variables using the belief propagation algorithm. A ...