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How do you derive the moment generating function of an exponential distribution?
Wiki User
∙ 12y ago
(1/x)e^-(y/x)
Wiki User
∙ 12y ago
To derive the moment generating function of an exponential distribution, you can use the definition of the moment generating function E(e^(tX)) where X is an exponential random variable with parameter λ. Substitute the probability density function of the exponential distribution into the moment generating function formula and simplify the expression to obtain the final moment generating function for the exponential distribution, which is M(t) = λ / (λ - t) for t < λ.
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