Mathematics, 27.07.2021 14:00, fnaflover8505
A computer system uses passwords that are exactly six characters and each character is one of the 26 letters (a–z) or 10 integers (0–9). Suppose that 10,000 users of the system have unique passwords. A hacker randomly selects (with replace- ment) one billion passwords from the potential set, and a match to a user’s password is called a hit. (a) What is the distribution of the number of hits? (b) What is the probability of no hits? (c) What are the mean and variance of the number of hits?
Answers: 2
and 
.
hits is approximately 
(or equivalently, approximately 
.)
. The variance of the number of hits is approximately 
(not the same number as the mean.)
possible passwords in this set. (Approximately two billion possible passwords.)
randomly-selected passwords would have an approximately 
chance of matching one of the users' password. 
:
.
denote a hit and 
trials (a billion trials) and 
.
is between 
would approach 
as the value of 
approaches infinity.) 
.
.
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