The number of ships X that arrives at a port during a day has proven to be given by a Poisson distribution with E(X) = 2. Which number of ships has largest probability of arriving on a certain day?
Attempt.
\(
p(x;2) = \frac{e^{-2} \cdot 2^x}{x!}
\)
The formula yields
p(0;2) = 0.135
p(1;2) = 0.270
p(2;2) = 0.270
p(3;2) = 0.180
and then values of p approaching zero. The numbers of ships most likely to arrive are 1 or 2.
The port can handle at most 3 ships a day. Redundant ships are sent to another port.
What's the expected number of ships that are handled each day?
Expected number= 1*0.27 + 2*0.27 + 3* 0.18 = 1.35 (Correct: 1.782)
Which capacity is necassary to be able to handle all incoming ships on a day with 90% certainty?
No idea...
Attempt.
\(
p(x;2) = \frac{e^{-2} \cdot 2^x}{x!}
\)
The formula yields
p(0;2) = 0.135
p(1;2) = 0.270
p(2;2) = 0.270
p(3;2) = 0.180
and then values of p approaching zero. The numbers of ships most likely to arrive are 1 or 2.
The port can handle at most 3 ships a day. Redundant ships are sent to another port.
What's the expected number of ships that are handled each day?
Expected number= 1*0.27 + 2*0.27 + 3* 0.18 = 1.35 (Correct: 1.782)
Which capacity is necassary to be able to handle all incoming ships on a day with 90% certainty?
No idea...
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