An irregularly shaped object of unknown area A is located in the unit square 0 ≤ x ≤ 1,0 ≤ y ≤ 1 . Consider a random point distributed uniformly over the square; let Z=1 if the point lies inside the object and Z=0 otherwise. Show that E(Z)=A . How could A be estimated from a sequence of n independent points uniformly distributed on the square?
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