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4. (30 points) Suppose N is the number of visitors to a web site that purchase an item out of the next 64 visitors. Assume that whether a visitor purchases an item or not has probability p and is independent of what the other Visitors do. (a) What is the probability mass function of N? (b) Assume p = 3/64. Approximate IP{N = 1} using either a Gaussian or Poisson approximation, whichever is more appropriate. (c) Assume p = 1/2. Approximate lP'{N = 32} using either a Gaussian or Poisson approximation, whichever is more appropriate