(Open-ended) Monte Carlo evaluation of an integral was introduced in Example A of Section 5.2….

(Open-ended) Monte Carlo evaluation of an integral was introduced in Example A of Section 5.2. Refer to that example for the following notation. Try to interpret that method from the point of view of survey sampling by considering an “infinite population” of numbers in the interval [0, 1], each population member x having a value f (). Interpret ˆI( f ) as the mean of a simple random sample. What is the standard error of ˆI( f )? How could it be estimated? How could a confidence interval for I( f ) be formed? Do you think that anything could be gained by stratifying the “population?” For example, the strata could be the intervals [0, .5) and [.5, 1]. You might find it helpful to consider some examples.

 

 

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