Probability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables
نویسندگان
چکیده
منابع مشابه
Probability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables
In this article we continue formalizing probability and randomness started in [13], where we formalized some theorems concerning the probability and real-valued random variables. In this paper we formalize the variance of a random variable and prove Chebyshev’s inequality. Next we formalize the product probability measure on the Cartesian product of discrete spaces. In the final part of this ar...
متن کاملProbability Generating Functions for Discrete Real Valued Random Variables
The probability generating function is a powerful technique for studying the law of finite sums of independent discrete random variables taking integer positive values. For real valued discrete random variables, the well known elementary theory of Dirichlet series and the symbolic computation packages available nowadays, such as Mathematica 5 TM, allows us to extend to general discrete random v...
متن کاملProbability on Finite Set and Real-Valued Random Variables
One can prove the following four propositions: (1) Let X be a non empty set, S1 be a σ-field of subsets of X, M be a σ-measure on S1, f be a partial function from X to R, E be an element of S1, and a be a real number. Suppose f is integrable on M and E ⊆ dom f and M(E) < +∞ and for every element x of X such that x ∈ E holds a ≤ f(x). Then R(a) ·M(E) ≤ ∫ f E dM. (2) Let X be a non empty set, S1 ...
متن کاملAcceptable random variables in non-commutative probability spaces
Acceptable random variables are defined in noncommutative (quantum) probability spaces and some of probability inequalities for these classes are obtained. These results are a generalization of negatively orthant dependent random variables in probability theory. Furthermore, the obtained results can be used for random matrices.
متن کاملProbability Models.S2 Discrete Random Variables
For a particular decision situation, the analyst must assign a distribution to each random variable. One method is to perform repeated replications of the experiment. Statistical analysis provides estimates of the probability of each possible occurrence. Another, and often more practical method, is to identify the distribution to be one of the named distributions. It is much easier to estimate ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2010
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-010-0026-6