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 ...

Extropy has emerged as a pivotal measure in the quantification of uncertainty, serving as a complementary counterpart to the traditional concept of entropy. Unlike entropy, which is widely used to ...

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 ...

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

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

Solve Real-World Problems With Applied Statistics. Applied Statistics is the implementation of statistical methods, techniques, and theories to real-world problems and situations in several fields, ...