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Suppose log(T) ∼ N(µ,σ^2). Find E(T) and Var(T).

I know I have to use the moment generating functions and probably do some transformations but I get confused at how to do so, can someone help me a little please?

baoiba
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  • If $T$ follows the $T$ distribution, then $\log(T)$ is not normal. What do you mean by "$\log(T) \sim N(\mu, \sigma^2)$"? – angryavian Oct 10 '20 at 00:37
  • My mistake, it actually doesn't follow the t-distribution. I edited the question! – baoiba Oct 10 '20 at 00:40
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    This is answered using MGFs here: https://math.stackexchange.com/a/1613828/43949 . On that page you can find an alternate answer using the PDF directly. – angryavian Oct 10 '20 at 00:48

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