This problem covers Sect. 3.2. Several \"named distributions\" are involved. The

Question

This problem covers Sect. 3.2. Several "named distributions" are involved. The recommended notation is: Suppose that visits (a.k.a. "signals") in a weather web page form a Poisson process with an average of 00 visits in each 3 hour period (this in how often the page is updated). What is the intensity of the process? What is the average number of visits in a 24 h day? What is the probability that there were at least three visits between 7 a.m. and 7:12 a.m.? At some point the page crashed and then it restored. What in the probability that the 6th visit happened within 5 minutes from the restoration? Whit Is the average waiting time for the 6th visit after the restoration of the page?

Explanation / Answer

from the possion disturbution

p(x>=1)=1-p(x=0)

p(x>=1)=1- e^-3*(3^0)/0!

=1-0.0498=0.9502

b) for 3 hours the avg number of visits is 90

then for 24 hours the avg number of visits is 24*90/3

then we will get answer is 720

c)for 3 hours the avg number of visits is 90

then from 7 to 7.12 is means 12 minutes

90/180sec=0.5

then for 12 minutes is 6 visits

the probility of atleat 3 visits means

d)the probility of 6th visit after 5 minutes is

0.5*5=2.5

then 2.5/180=0.013

the avg waiting time for 6 visit is

is 0.013*180=2.5 mins

3/6=0.5

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