1) Exponential Distribution a) The amount of time until the next earthquake occurs in a certain country is known to be exponentially distributed with =10 years. i) What is the probability that the country won't see another earthquake for more than 20 years? ii) What is the average length of time between earthquakes in this country? b) A research study shows that the lifetime of the computers at a certain university is exponentially distributed with an average of 4 years. i) A lab acquires 10 university computers. What is the probability that exactly half of them are still functioning after 6 years? (Hint: the probability of x successes after n trials...what is p ?) ii) What is the variance in computer lifetimes at this university?.