(a) Z = X-Y Calculate the variance of Z. »»»» 15+13=28
(b) Calculate Variance{Z+Y+Y+Y} »»»» 15+4× 13
(a) Out of N=90000 points, H hit the sphere.
What is the std. dev. of the random variable (H/N)?
»»»» sqrt(0.5236×0.4764/90000) = 0.001664...
(b) What is the least N that will assure the standard deviation of
(H/N) is no more than 10^{-5}
»»»» Solve 10^{-5} = Z×sqrt(0.5236×0.4764/N)
»»»» N = (4×0.5264×10^{10}) 5541939200 :: 5.54x10^{9}
((For grading this exam, Z=2 is accepted. For serious Monte
Carlo work, Z should be at least 3.))