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An insurance company determines that N, the number of claims received in a week, is a random variable with P[N = n] = 1/2n+1, where n > 0 . The company also determines that the number of claims received in a given week is independent of the number of claims received in any other week. Determine the probability that exactly seven claims will be received during a given two week period.

  1. 1/256
  2. (B)1/128
  3. (C) 7/512
  4. (D) 1/64
  5. (E)1/32

Solution:  D

Let N1 and N2 denote the number of claims  during  weeks one and two, respectively.

Then since  N1 and N2 are independent,