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How do you find the expectation and variance of the random variable e^X in terms of μ and σ?

Integrating the entire normal function with the f(x) is it?

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- Thread starter kensaurus
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How do you find the expectation and variance of the random variable e^X in terms of μ and σ?

Integrating the entire normal function with the f(x) is it?

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HallsofIvy

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Ray Vickson

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How do you find the expectation and variance of the random variable e^X in terms of μ and σ?

Integrating the entire normal function with the f(x) is it?

Yes. However, it is best to find once and for all the expectation of exp(k*Z), where k is a constant and Z is a standard normal. Then, a general X has the form X = μ + σZ, so finding E[exp(X)] as exp(μ) * E[exp(σZ)] will be straightforward. As to Var(X): the easiest way is to use the standard theorem which that states that Var(Y) = E[Y

RGV

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