What is the distribution of the number of failures by, Basic Statistics

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What is the distribution of the number of failures by

A system has a random number of ?aws that we will suppose is Poisson distributed with mean c. Each of these ?aws will, independently, cause the system to fail at a random time having distribution G. When a system failure occurs, suppose that the ?aw causing the failure is immediately located and ?xed.

(a) What is the distribution of the number of failures by time t?

(b) What is the distribution of the number of ?aws that remain in the system at time t?

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