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Abstract
In this thesis, we considered the distribution of the sum of Bernoulli random variables in two different cases. First, we discussed the case of independent Bernoulli random variables and proposed several new approximations. Secondly, we considered the case of dependent Bernoulli random variables in a certain two state binary Markov chain and proposed some new approximations also. Although in both cases, recurrence relations can be used to compute the exact distribution, this can be quite time consuming for large number of Bernoulli random variables. Also, closed form equations for the exact distribution are generally not available. In the case of independent Bernoulli random variables, the modified Taylor series method performed the best in a majority of the cases against the traditional methods including the three parameter binomial method provided by Pekoz et al. [2009]. In the case of dependent Bernoulli random variables, we compared the new approximations proposed to the exact distribution. Each method performed well, under certain conditions. However, in general, the Double Poisson method performed the best.
