3-91. A computer system uses passwords that are exactly six characters and each

Question

3-91. A computer system uses passwords that are exactly six characters and each character is one of the 26 letters (a-2) or 10 integers (0-9). Suppose there are 10,000 users of the system with unique passwords. A hacker randomly selects (with replacement) 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?

Explanation / Answer

a) X- number of hits

X follows binomial distribution

n = 10000, p = (1/36)^6

b) P(X = 0) = (1-p)^n

= (1 - (1/36)^6 )^10000

= 0.9999954

c) mean = np = 10000/36^6 = 0.000004593

variance = npq = 10000/36^6 * (1- 1/36^6) =0.00000459393

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