Problem 6.1 Let X be a continuous random variable representing the (exact) lifetime of a hard drive, measured in years. A simple1 model for X is that is an Exponential()\\) random variable. You may assume that your brand of hard drive has an average lifetime of 100 years. (a) What is the probability that the drive lasts less than 5 years? (b) Consider the event B : {X 2 3;} that your hard drive has already lasted 3; years. What is the conditional PDF f XI 3(37)? Interpret the intuition behind your formula. (0) Say that your hard drive has already lasted y years. What is the probability that it fails before y + 1 years