Refer to Exercise 3.83. Find the mean and the variance of

QUESTION:

Problem 84E

Refer to Exercise 3.83. Find the mean and the variance of Y , the number of the trial on which the correct password is first identified.

Reference

The secretary in Exercises 2.121 and 3.16 was given n computer passwords and tries the passwords at random. Exactly one of the passwords permits access to a computer file. Suppose now that the secretary selects a password, tries it, and—if it does not work—puts it back in with the other passwords before randomly selecting the next password to try (not a very clever secretary!). What is the probability that the correct password is found on the sixth try?

Reference

A new secretary has been given n computer passwords, only one of which will permit access to a computer file. Because the secretary has no idea which password is correct, he chooses one of the passwords at random and tries it. If the password is incorrect, he discards it and randomly selects another password from among those remaining, proceeding in this manner until he finds the correct password.

a What is the probability that he obtains the correct password on the first try?

b What is the probability that he obtains the correct password on the second try? The third try?

c A security system has been set up so that if three incorrect passwords are tried before the correct one, the computer file is locked and access to it denied. If n = 7, what is the probability that the secretary will gain access to the file?

3.16 The secretary in Exercise 2.121 was given n computer passwords and tries the passwords at random. Exactly one password will permit access to a computer file. Find the mean and the variance of Y, the number of trials required to open the file, if unsuccessful passwords are eliminated (as in Exercise 2.121).