Problem 98a

Given information

Use the following information to answer the next three exercises. The average lifetime of a certain new cell phone is three years. The manufacturer will replace any cell phone failing within two years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution.

During the years , a total of  earthquakes of magnitude greater than  have occurred in Papua New Guinea. Assume that the time spent waiting between earthquakes is exponential.

Step-by-step explanation

The total number of months from will be,

Since, earthquakes will occur in in hence earthquake will occur,

Therefore, the random variable will follow, the exponential distribution is given by

The cumulative distribution function exponential distribution is given by,

Required probability can be calculated by,

Therefore, the probability that next earthquake occurs within the next three months

.