Organisms are present in ballast water discharged from a ship according to a Poi

Question

Organisms are present in ballast water discharged from a ship according to a Poisson process with =10/m 3 .

a) Determine the probability that a 1 m3 of discharge contains exactly 5 organisms. You may use either the Poisson formula or table A.2.

b) Consider an area of 1.5 m3 . Determine for the rate of organisms in a 1.5 m3 area of discharge.

c) Determine the probability that a 1.5 m3 of discharge contains exactly 5 organisms. You may use either the Poisson formula or table A.2.

d) For what amount of discharge would the probability of containing 0 organisms be 0.001. Hint: write P(X = 0) as a function of =t , then solve for t.

Explanation / Answer

Organisms are present in ballast water discharged from a ship according to a Poisson process with =10/m 3 .

(a0 For discharge = 1 m3

Mean Organisms present = 10 * 1 = 10

so Pr( X = 5) = POISSON ( X = 5; 10) = 0.0378

(b) Area = 1.5 m3

Mean () for the rate of organisms in a 1.5 m3 area of discharge. = 1.5 * 10 = 15

(c) Pr (X = 5; 15) = POISSON ( X = 5, 15) = 0.0019

(d0 Lets say amount of discharge is t

so Mean value of organisms = t

so Pr( X = 0) = e- x/ x! = e- = 0.001

= - ln(0.001) = 6.91

so 6.91 = t  

t = 6.91/10 = 0.69 m3 is the amount of discharge

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