Addition of freely independent random variables

Addition of Freely Independent Random Variables

Pairwise Independent Random Variables

In this lecture we discuss how to derandomize algorithms. We will see a brute force algorithm (enumeration) for derandomization. We will also see that some random algorithms do not need true randomness. Specifically, we will see an example where only pairwise random bits are needed. Next, we will see how we can generate pairwise random values and how this conservation on the amount of randomnes...

Independent random variables

1 Last two lectures ¯ probability spaces ¯ probability measure ¯ random variables and stochastic processes ¯ distribution functions ¯ independence ¯ conditional probability ¯ memoriless property of geometric and exponential distributions ¯ expectation ¯ conditional expectation (double expectation) ¯ mean-square estimation 1

Conditionally independent random variables

In this paper we investigate the notion of conditional independence and prove several information inequalities for conditionally independent random variables. Keywords— Conditionally independent random variables, common information, rate region.

Estimating Sums of Independent Random Variables

The paper deals with a problem proposed by Uriel Feige in 2005: if X1, . . . , Xn is a set of independent nonnegative random variables with expectations equal to 1, is it true that P ( ∑n i=1 Xi < n + 1) > 1 e ? He proved that P ( ∑n i=1Xi < n + 1) > 1 13 . In this paper we prove that infimum of the P ( ∑n i=1Xi < n + 1) can be achieved when all random variables have only two possible values, a...