A man has a set of n keys, one of which fits the door to his apartment. He tries the keys randomly, throwing away each ill-fitting key that he tries until he finds the key that fits. That is, he chooses keys randomly from among those he has not yet tried. This way he is sure to find the right key within n tries. Let T be the number of times he tries keys until he finds the right key. Write closed-form expressions for E[T] and Var[T]. Hint: Write T as a linear combination of indicator variables.