(Expectation) A box contains n tickets, numbered 1, 2, ..., n. A ticket is drawn at random from the box, its number is registered, and the ticket is returned to the box. Another ticket is drawn at random from the box, again its number is registered, and the ticket is returned to the box. This procedure is repeated until first such moment T when all n numbers have been registered. Obviously, the moment T can be represented as the following sum T=T, + T,+T, +...+.. where T, = 1 is waiting time till the "first new number" is obtained; T, is the waiting time till another "new" number is obtained, i.e., a number different from the previous one; T3 is the waiting time till yet another "new" number is obtained, different from the previous two; etc. a) What is the distribution of i) T, ? ii) T3? iii) 7.? b) Find the expected value ET