I am quite stuck here, but well I am trying my best.
The Web page of a teacher receives hits from his students according to a poisson process with rate λ=10 visits/day . Also, his colleagues , are vititng his page with rate 2 visits per/day .
1) What is the probability the visits to exceed 10 in a day?
2) What is the probability no student visits his page into 10 hours interval ?
3) Suppose that every student who visits the site , press the link with teachers publications with chance 2/5. What is the probability into a day that only one student pressed that link?
My attempted Solution:
1) To begin with I turn the days into hours , for my convenience. So I assume that λ1= 10/24 and λ2=2/24=1/12 .
Since the question is not very clear to me... I think that we just need
P((s,s+24))= P((s,s+24))-N(s) >10) =P(N(24)> 10) .
here λ=λ1+λ2 = 1/2 . But, I am not sure how to continue from this point. Should I take some integral from 10 to inf of e^(-λs) * (λs)^x/x! dx ?
Couldn't also I say that its the probability 1-(p(0)+p(1)+...+p(10) )? Although this might take loads of time .
2) So for this question, λ=10/24 . And probably, we need something very very simple ,although for some reason I believe that I am missing something here, but anyway. This: P(0 student visits on (0,10)) so it should be e^100/24 =~ e^-(4.1)