In Example 5.5.16, a normal approximation to the negative binomial distribution was given. Just as with the normal approximation to the binomial distribution given in Example 3.3.2, the approximation might be improved with a "continuity correction." For XiS defined as in Example 5.5.16, let Vn = ∑n i =1. For n = 10,p = .7, and r = 2, calculate P(Vn = v) for v = 0,1,.... 10 using each of the following three methods.
(a) Exact calculations
(b) Normal approximation as given in Example 5.5.16
(c) Normal approximation with continuity correction