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Prob & Stats, Lec 17A: Distribution of Sum of 2 Independent Random Variables (Exponential & Uniform)
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This is a preview of the Central Limit Theorem! Let X and Y be two independent and identically distributed random variables. What is the distribution of their sum S = X + Y? We can use the CDF Method and the assumption of independence to find out. We do two examples: 1) X and Y each have exponential distributions with mean 1, and 2) X and Y each have uniform distributions over the interval (0,1). The results point toward the Central Limit Theorem. We can also determine the distribution of the sample mean "X bar", which is a statistic based on a random sample from a population.
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