Nneetquant
Get started

Second moment via the MGF

MediumRandom VariablesCalculus~5m

X∼Exp(3)X\sim\text{Exp}(3) (rate λ=3\lambda=3). Using its moment-generating function, compute the second moment E[X2]E[X^2]. (to 4 decimals)

Show hints (2)+
  1. Derive M(t) = λ/(λ − t), then E[X²] = M''(0).
  2. M''(t) = 2λ/(λ − t)³; evaluate at t = 0.

Answer

Reveal answer →

0.2222 (± 0.0005)

Create a free account to see the full worked solution and track your progress.

Create a free account

Interview format: Hedge Fund Quant, Systematic & Data-Driven Trading

Related questions