David Harper is the CEO and founder of Bionic Turtle. He is also a published author with a popular YouTube channel on expert finance topics. Almost regardless of your view about the predictability or ...

So far, you learned about discrete random variables and how to calculate or visualize their distribution functions. In this lesson, you'll learn about continuous variables and probability density ...

This paper is concerned with the determination of tight lower and upper bounds on the expectation of a convex function of a random variable. The classic bounds are those of Jensen and ...

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, ...

A continuous random variable is a type of variable that can take on any value within a given range. Unlike discrete random variables, which have a countable number of outcomes, continuous random ...

This is a preview. Log in through your library . Abstract Jensen gave a lower bound to Eρ(T), where ρ is a convex function of the random vector T. Madansky has obtained an upper bound via the theory ...