Solution Found!
An article in Information Security Technical Report
Chapter 3, Problem 105E(choose chapter or problem)
An article in Information Security Technical Report [“Malicious Software—Past, Present and Future” (2004, Vol. 9, pp. 6–18)] provided the following data on the top 10 malicious software instances for 2002. The clear leader in the number of registered incidences for the year 2002 was the Internet worm “Klez,” and it is still one of the most widespread threats. This virus was first detected on 26 October 2001, and it has held the top spot among malicious software for the longest period in the history of virology. The 10 most widespread malicious programs for 2002
(Source: Kaspersky Labs).
Suppose that 20 malicious software instances are reported. Assume that the malicious sources can be assumed to be independent.
(a) What is the probability that at least one instance is “Klez?”
(b) What is the probability that three or more instances are “Klez?”
(c) What are the mean and standard deviation of the number of “Klez” instances among the 20 reported?
Questions & Answers
QUESTION:
An article in Information Security Technical Report [“Malicious Software—Past, Present and Future” (2004, Vol. 9, pp. 6–18)] provided the following data on the top 10 malicious software instances for 2002. The clear leader in the number of registered incidences for the year 2002 was the Internet worm “Klez,” and it is still one of the most widespread threats. This virus was first detected on 26 October 2001, and it has held the top spot among malicious software for the longest period in the history of virology. The 10 most widespread malicious programs for 2002
(Source: Kaspersky Labs).
Suppose that 20 malicious software instances are reported. Assume that the malicious sources can be assumed to be independent.
(a) What is the probability that at least one instance is “Klez?”
(b) What is the probability that three or more instances are “Klez?”
(c) What are the mean and standard deviation of the number of “Klez” instances among the 20 reported?
ANSWER:
Solution 105E
Step1 of 4:
Let us consider a random variable X it presents the number of instances which are ‘Klez’. Also we have n = 20 and p = 61.22%
= 0.6122.
Here our goal is:
a). We need to find the probability that at least one instance is “Klez.”
b). We need to find the probability that three or more instances are “Klez.”
c). We need to find the mean and standard deviation of the number of “Klez” instances among the 20 reported.
Step2 of 4:
a).
Suppose that a random variable X follows binomial distribution with parameters ‘n and p’.
Then, the probability mass function of binomial is distribution is given by:
x = 0,1,2,...,n.
Here, we have n = 20, p = 0.6122.
Consider,
The probability that at least one instance is “Klez” is given by: