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Mathematics, 26.10.2021 02:10 salam4704

3. (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 + T2 + T2 + ... + In,
where Ti = 1 is waiting time till the first β€œnew” number is obtained; T2 is the
waiting time till another β€œnew” 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) T; ? iii) Tn?
b) Find the expected value ET.

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3. (Expectation) A box contains n tickets, numbered 1,2, ..., n. A ticket is drawn at random from...
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