Let X be a continuous random variable representing the (exact) lifetime of your TV set. measured in years. A simple model for X is that is an Exponential) random variable. You may assume that your brand of TV has an average lifetime of 20 years. (a) What is the probability that the TV fails in the rst year? (b) What is the probability that it lasts more than 5 years? {0) Consider the event 3 = {X 23 10} that your TV has already lasted 10 years. What is the conditional PDF fx|3($)? Interpret the intuition behind your formula. {(1) Assume your TV has already lasted 10 years. What is the probability that it fails during the next year