Fuzzy statistics and random variables represent a progressive fusion of traditional probability theory with the principles of fuzzy logic, enabling the treatment of imprecision and vagueness inherent ...

Explain why probability is important to statistics and data science. See the relationship between conditional and independent events in a statistical experiment. Calculate the expectation and variance ...

Let $W_{n}\coloneq \sum_{j=1}^{n}Z_{j}$ be a sum of independent integer-valued random variables. In this paper, we derive an asymptotic expansion for the probability ...

A behind-the-scenes blog about research methods at Pew Research Center. For our latest findings, visit pewresearch.org. Identifying causal relationships from observational data is not easy. Still, ...

Learn how representative samples and random samples differ and why combining them minimizes sampling bias for accurate data.

CATALOG DESCRIPTION: Fundamentals of random variables; mean-squared estimation; limit theorems and convergence; definition of random processes; autocorrelation and stationarity; Gaussian and Poisson ...

Melissa Horton is a financial literacy professional. She has 10+ years of experience in the financial services and planning industry. Robert Kelly is managing director of XTS Energy LLC, and has more ...