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Assume that a Web site changes its content according to
Chapter 3, Problem 113E(choose chapter or problem)
Problem 113E
Assume that a Web site changes its content according to the distribution in Exercise 3-34. Assume that 10 changes are made independently.
(a) What is the probability that the change is made in less than 4 days in 7 of the 10 updates?
(b) What is the probability that the change is made in less than 4 days in 2 or fewer of the 10 updates?
(c) What is the probability that at least one change is made in less than 4 days? (d) What is the expected number of the 10 updates that occur in less than 4 days?
3-34.The distribution of the time until a Web site changes is important to Web crawlers that search engines use to maintain current information about Web sites. The distribution of the time until change (in days) of a Web site is approximated in the following table.
Days until Changes |
Probability |
1.5 |
0.05 |
3.0 |
0.25 |
4.5 |
0.35 |
5.0 |
0.20 |
7.0 |
0.15 |
Calculate the probability mass function of the days until change.
Questions & Answers
QUESTION:
Problem 113E
Assume that a Web site changes its content according to the distribution in Exercise 3-34. Assume that 10 changes are made independently.
(a) What is the probability that the change is made in less than 4 days in 7 of the 10 updates?
(b) What is the probability that the change is made in less than 4 days in 2 or fewer of the 10 updates?
(c) What is the probability that at least one change is made in less than 4 days? (d) What is the expected number of the 10 updates that occur in less than 4 days?
3-34.The distribution of the time until a Web site changes is important to Web crawlers that search engines use to maintain current information about Web sites. The distribution of the time until change (in days) of a Web site is approximated in the following table.
Days until Changes |
Probability |
1.5 |
0.05 |
3.0 |
0.25 |
4.5 |
0.35 |
5.0 |
0.20 |
7.0 |
0.15 |
Calculate the probability mass function of the days until change.
ANSWER:Answer
Step 1 of 4
(a)
Assume that a Web site changes its content according to the distribution given in the below table.
Assume that changes are made independently.
Days until Changes |
Probability |
1.5 |
0.05 |
3.0 |
0.25 |
4.5 |
0.35 |
5.0 |
0.20 |
7.0 |
0.15 |
We are asked to find the probability that the change is made in less than days in
of the 10 updates.
Let denote the number of the 10 changes made in less than 4 days.
We need to find
Hence follows a binomial distribution which we can write,
The random variable that equals the number of trials that result in a success is a binomial random variable with parameters
The probability mass function (PMF) of is,
………………(1)
The probability that the change is made in less than
days is from the table,
We have given
Hence the substitute the above values into equation (1),
Hence the probability that the change is made in less than days in
of the 10 updates is