Questions / Quant research, Stochastic calculus & linear algebra
Moments of Brownian motion
What is E[W₄²]?
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Answer: 4 variance units
- W₄ ~ N(0, 4).
- E[W₄²] = Var(W₄) = 4.
Interview shortcut. Mean zero, so E[W²] = Var = t.
Takeaway. E[W_t²] = t.
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