Abstract
This chapter discusses independent random variables. The partial sums of a finite sequence of independent random variables cannot be large unless the total sum is. The chapter presents an estimation of the sum of independent random variables. In connection with the rate of convergence, an important problem is to find conditions ensuring exponential convergence rates, that is, ensuring the validity of the inequality. In the case of a strong law, a good necessary and sufficient condition is unknown. The fundamental law on identically distributed random variables is because of Kolmogorov. The chapter also describes the concept of weighted averages.
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