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Under which of the following situations would you prefer bootstrapping to pure simulation?
A
If you have a very small sample of actual data
B
If the distribution of the actual data is unknown
C
If the distribution of the data is known exactly
D
All the above
Explanation:
When the properties of the actual data are unknown, bootstrapping may be preferred to pure simulation since it would be very difficult to find an appropriate distribution from which to make the random draws needed under pure simulation.
Detailed Explanation:
Bootstrapping is a resampling technique that uses the empirical distribution of the actual data to create new samples. This is particularly useful when:
Pure simulation requires specifying a theoretical distribution from which to draw random samples. If the true distribution is unknown, it's difficult to choose an appropriate distribution for simulation, making bootstrapping a better choice.
Option A is incorrect because bootstrapping typically requires a reasonably sized sample to work effectively. With very small samples, bootstrapping may not provide reliable results.
Option C is incorrect because if the distribution is known exactly, pure simulation would be more appropriate as you can directly sample from the known distribution.
Option D is incorrect because not all situations favor bootstrapping over pure simulation.