example 1

3 Analysis Consider the following question: You shoot a square (-1,1)2. Suppose your shot is uniform in this square, then what is the probability you have a successful shot? We say your shot is successful, if your shot belongs to the unit ball B1. The answer is Area of B Prob of succesful shot = - Area of (-1,1)2 = : This means that, as long as one can approximate probability of successful shot, one can approximate a by multiplying 4. This can be done by computer: N is total number of samples >n is number of hits Algorithm 1 MC estimation of 1: procedure MCPI(N) 2: no 3: for i = 1...N do 4: generate two numbers X, Y from U(-1,1) 5: if x2 + y2 n is number of hits Algorithm 1 MC estimation of 1: procedure MCPI(N) 2: no 3: for i = 1...N do 4: generate two numbers X, Y from U(-1,1) 5: if x2 + y2