Question

Web crawlers need to estimate the frequency of changes to Web sites to maintain a current index for Web searches.Assume that the changes to a Web site follow a Poisson process with a mean of 3.5 days.(a) What is the probability that the next change occurs in less than 20 days?(b) What is the probability that the time until the next change is greater 7.0 days?(c) What is the time of the next change that is exceeded with probability 90%?21) What is the probability that the next change occurs in less than 10.0 days, given that it has not yet occurred after 3.0ays?

Answer 1

0.93471,0.02674,0,0.9945

Explanation:

giventhat web crawlers need to estimate the frequency of changes to Web sites to maintain a current index for Web searches.

X the changes to a web site is a Poisson variable with mean = 3.5 days

a) the probability that the next change occurs in less than 20 days

=
`P(X<20)\\=0.93471`

b) the probability that the time until the next change is greater 7.0 days

=
`P(X>7) \\=0.02674`

c) P(X>c) =0.90

Only for c=0 this is true.

d) the probability that the next change occurs in less than 10.0 days, given that it has not yet occurred after 3.0ays

=
`P(X<10/P(X\geq 3)\\=(P(3\leq x<10))/(P(x\geq 3) \\=(0.99628-0.3208)/(0.6792) \\=0.9945`