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Theoretical Variance: Sampling Distribution of the Mean

A number of students in Johns Hopkins University Data Science Specialization Statistical Inference course have asked questions about the theoretical variance for the distribution of sample means taken from an exponential distribution.

Within the assignment instructions we are told to use a value of lambda = .2 for the simulations we generate as we validate the Central Limit Theorem.

Given the assigned value of lambda, we derive the value of the theoretical variance as follows: