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...

This paper presents a deterministic approach for performance assessment of different province’s road safety level at Iran. A data envelopment analysis (DEA) model considering undesirable input and output indices and a multivariate statistical method, principle component analysis (PCA) are used in this paper, while previous studies do not use composite PCA-DEA method and undesirable input and ou...

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

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.