An insurance company determines that N, the number of claims received in a week,

Question

An insurance company determines that N, the number of claims received in a week, is a random variable with: P r(N = n) = 1/(2 ^(n+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. Hint: consider all possible combination of the number of claims of the first week and that of the second week to make exactly 7 claims together.

Explanation / Answer

An insurance company determines that N, the number of claims received in a week, is a random variable with: P r(N = n) = 1/(2 ^(n+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. Hint: consider all possible combination of the number of claims of the first week and that of the second week to make exactly 7 claims together.

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