Monte Carlo simulation approximates an unknown expectation value by an arithmetic mean, computed from a random sample. This mean can be understood as the expectation value with respect to the estimated probability density

Show that for an arbitrary function h(x), the arithmetic mean

is the exact expectation value with respect to f?(x), and that f?(x) itself is an unbiased estimator for the true density f(x).

Transcribed Image Text:

ĵ(x) = ΝΣ -xω) n=1 ΣΗν) he n=1