Respuesta :
Answer:
Step-by-step explanation:
Given that a fisherman catches fish according to a Poisson process with rate lambda = 0.6 per hour.
The fisherman will keep fishing for two hours.
Since he continues till he gets atleast one fish, we can calculate probability as follows:
(a) Find the probability that he stays for more than two hours.
= Prob (x=0) in I two hours and P(X≥1) in 3rd hour
=P(x=0)*P(X=0)*P(X≥1) (since each hour is independent of the other)
= [tex]0.5488^2*(1-0.8781)\\\\=0.2645[/tex]
(b) Find the probability that the total time he spends fishing is between two and five hours.
Prob that he does not get fish in I two hours * prob he gets fish between 3 and 5 hours
=[tex]P(0)^2 *F(1)^3\\=0.5488^2*0.2645^3\\=0.00557[/tex]
(c) Find the expected number offish that he catches.
Expected value in Geometric distribution = [tex]\frac{1-p}{p}[/tex], where p = prob of getting 1 fish in one hour
= [tex]\frac{0.6}{1-0.6} \\=3[/tex]
(d) Find the expected total fishing time, given that he has been fishing for four hours.
= Expected fishing time total/expected fishing time for 4 hours
=3/0.6*4
= 1.25 hours
