Random Variable: A measurable function that maps outcomes in a probability space to real numbers, thereby enabling quantitative analysis of random events.

Probability, statistics, reliability and decision with applications in engineering. Probability of events, discrete and continuous random variables, probability density functions and distributions, ...

Boyan Dimitrov, Stefanka Chukova, David Green, Jr. Periodic random environments and mechanisms of their effect on imbedded random variables are discussed. The variables under consideration represent ...

Discover what a log-normal distribution is, its financial applications, and how to calculate it, including using Excel for ...

Albert Madansky, Bounds on the Expectation of a Convex Function of a Multivariate Random Variable, The Annals of Mathematical Statistics, Vol. 30, No. 3 (Sep., 1959), pp. 743-746 ...

The world is full of uncertainty: accidents, storms, unruly financial markets, noisy communications. The world is also full of data. Build foundational knowledge of data science with this introduction ...

Sample space and events, probability measure and probability space, random variable as a measurable function, distribution function of a random variable, discrete and continuous-type random ...

Key Takeaways Expected value describes the long-term average level of a random variable based on its probability distribution.