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 ...

In the early development of probability theory, only discrete random variables (although not called random variables at the time) were considered. Isaac Newton (1643-1727) considered the idea of ...

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 ...

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 ...

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 ...

Marketing research professionals often use inferential or descriptive statistics to guide major marketing decisions. There are a number of statistical tests that explore the relationship between the ...