| Summary: | This paper aims to improve further on the work of Phu (2001), Aytar (2008), and Ghosal (2013). We propose a new
apporach to extend the application area of rough statistical convergence usually used in triple sequence of the Bernstein operator
of real numbers to the theory of probability distributions. The introduction of this concept in the probability of Bernstein
polynomials of rough statistical convergence, Bernstein polynomials of rough strong Cesàro summable, Bernstein polynomials of
rough lacunary statistical convergence, Bernstein polynomials of rough convergence, Bernstein polynomials of rough
statistical convergence, and Bernstein polynomials of rough strong summable to generalize the convergence analysis to
accommodate any form of distribution of random variables. Among these six concepts in probability only three convergences are
distinct Bernstein polynomials of rough statistical convergence: (1) Bernstein polynomials of rough lacunary statistical
convergence, (2) Bernstein polynomials of rough statistical convergence where Bernstein polynomials of rough strong
Cesàro summable is equivalent to Bernstein polynomials of rough statistical convergence, and (3) Bernstein polynomials of
rough convergence which is equivalent to Bernstein polynomials of rough lacunary statistical convergence. Bernstein
polynomials of rough strong summable is equivalent to Bernstein polynomials of rough statistical convergence.
Basic properties and interrelations of these three distinct convergences are investigated and some observations were made in
these classes and in this way we demonstrated that rough statistical convergence in probability is the more generalized concept
than the usual Bernstein polynomials of rough statistical convergence.
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