Spread of a lognormal raised to the fourth

HardRandom Variables Statistics~7m

Suppose $\ln X \sim \mathcal N(0, 1)$ . Find $\operatorname{Var}(X^4)$ . The answer has the form $e^{a} - e^{b}$ for positive integers $a, b$ ; find $a + b$ .

Show hints (2)+

$\ln(X^4)=4\ln X\sim\mathcal N(0,16)$ , so $X^4$ is lognormal with $\sigma^2=16$ .
Lognormal variance $=(e^{\sigma^2}-1)e^{2\mu+\sigma^2}=e^{32}-e^{16}$ .

Answer

Reveal answer →

Want the full step-by-step worked solution? It's part of Premium - along with a worked solution for every question in the bank.

Practise free Unlock solutions

Asked at: SIG, Two Sigma

Spread of a lognormal raised to the fourth

Answer

Related questions