The Journal of Earthquake Engineering modeled the time Y (in years) between major earthquakes occurring in the Iranian Plateau. One of the models considered had the following density function:

a. Show that the properties of a density function for a continuous random variable are satisfied for any constant c > 0.    

b. For one area of Iran, c was estimated to be Using this value, give the equation of the cumulative distribution function, F(y).

c. The earthquake system reliability at time t, R(t), is defined as R(t) = 1 – F(t). Find R(5) and interpret this probability.

Transcribed Image Text:

f(y) = ce , y > 0 -cy