  In this paper, we generalize the result on the average volume of random
polytopes with vertices following beta distributionsto the case of
non-identically distributed vectors. Specifically,we consider the convex hull
of independent random vectors in $\mathbb{R}^d$, where each vector follows a
beta distribution with potentially different parameters. We derive an
expression for the expected volume of these generalized beta--polytopes.
Additionally, we compute the expected value of a functional introduced by
Wieacker, which involves the distance of facets from the origin and their
volumes.Our results extend the findings of Kabluchko, Temesvari,and Th\"ale.
Key techniques used in the proofs include the Blaschke--Petkantschin formula,
Kubota's formula, and projections of beta distributed random vectors.
