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JAR
2008
88views more  JAR 2008»
13 years 6 months ago
Using Theorem Proving to Verify Expectation and Variance for Discrete Random Variables
Statistical quantities, such as expectation (mean) and variance, play a vital role in the present age probabilistic analysis. In this paper, we present some formalization of expect...
Osman Hasan, Sofiène Tahar
JCST
2010
189views more  JCST 2010»
13 years 28 days ago
Formally Analyzing Expected Time Complexity of Algorithms Using Theorem Proving
Probabilistic techniques are widely used in the analysis of algorithms to estimate the computational complexity of algorithms or a computational problem. Traditionally, such analys...
Osman Hasan, Sofiène Tahar
FM
2009
Springer
101views Formal Methods» more  FM 2009»
13 years 10 months ago
Formal Reasoning about Expectation Properties for Continuous Random Variables
Abstract. Expectation (average) properties of continuous random variables are widely used to judge performance characteristics in engineering and physical sciences. This paper pres...
Osman Hasan, Naeem Abbasi, Behzad Akbarpour, Sofi&...
STOC
2004
ACM
110views Algorithms» more  STOC 2004»
14 years 6 months ago
On sums of independent random variables with unbounded variance, and estimating the average degree in a graph
We prove the following inequality: for every positive integer n and every collection X1, . . . , Xn of nonnegative independent random variables that each has expectation 1, the pr...
Uriel Feige
APPROX
2010
Springer
213views Algorithms» more  APPROX 2010»
13 years 7 months ago
Constructive Proofs of Concentration Bounds
We give a simple combinatorial proof of the Chernoff-Hoeffding concentration bound [Che52, Hoe63], which says that the sum of independent {0, 1}-valued random variables is highly ...
Russell Impagliazzo, Valentine Kabanets