The article "Reliability-Based Service-Life Assessment of Aging Concrete Structures" (J. Structural Engr., 1993: 1600-1621) suggests that a Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is .5 year.
a. How many loads can be expected to occur during a 2-year period?
b. What is the probability that more than five loads occur during a 2-year period?
c. How long must a time period be so that the probability of no loads occurring during that period is at most .1?