Practice question · Multiple choice
Monte Carlo integration is hopeless in one dimension and indispensable in three hundred. What flips the verdict?
Hints
- A grid of 100 points per axis in 10 dimensions. How many points is that?
- Ask whether d appears anywhere in the Monte Carlo error formula.
Show the answer
D. Its 1/√N error is independent of dimension, unlike a grid's n^d
Why
100¹⁰ is 10²⁰ grid points and Monte Carlo's error does not contain d at all. The 1/√N rate is genuinely slow, a hundredfold more samples per extra digit, and it is the only thing that survives the curse of dimensionality, which is why finance and statistical physics run on it.
Practise Sequences and Series
The app has 6 more questions on this lesson, and keeps your place in the course. Computer Science I is free to start.
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