Earthquake recurrence in Iran. The Journal of Earthquake Engineering (Vol. 17, 2013) modeled the time x (in years)

between major earthquakes occurring in the Iranian Plateau. One of the models considered had the following LO8 density function:

f1x2 = .04e-.04x, x 7 0

a. Find E(x). Interpret the result.

b. Find the variance of x.

c. Use the empirical rule to estimate P1m - 2s 6 x 6 m + 2s2.

d. Find the actual probability, P1m - 2s 6 x 6 m + 2s2.

How does the answer compare to the result in part c?

e. The earthquake system reliability at time t, R(t), is defined as R1t2 = 1 - F1t2. Find R(5) and interpret this probability.