Description
1. Rizzo book (1st edition) Excercise 5.3, 5.4, 5.5, 5.9 and 5.10.
2. Monte Carlo method can be used to approximate the fraction of a d-dimensional
hypersphere which lies in the inscribed d-dimensional hypercube. Simulate with
different dimensions d = 2, 3, 4, . . . , 10. (Hint: use apply function.)
(1) Derive the formula for the EXACT values for the above problem for each ddimension.
(2) Using the above formula, approximate the value of π. Find the number of points
needed to approximate π to its 4-th digit for each dimension d. Set the random
seed with set.seed(123) at the beginning of your R code.
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