The number of casualties experienced by a deep draft marine vessel over a 3 year
ID: 3440731 • Letter: T
Question
The number of casualties experienced by a deep draft marine vessel over a 3 year period is modeled as a poisson random variable X with the mean equal to 0.03
a. find the variance of this random variable
b. what is the average number of casualties experienced by this vessel over a 3 year period?
c. write the probability statement and calculate the probability that a deepp draft vessel will have exactly one casualty in a 3 year time period?
d. write the probability statement and calculate the probability that a deepp draft vessel will have no casualties in a 3 year time period?
Explanation / Answer
a)
The variance of a Poisson variable is also the mean, 0.03. [ANSWER]
b)
Over a three year period, there is a mean of 0.03*3 = 0.03 [ANSWER]
C)
Note that the probability of x successes out of n trials is
P(x) = u^x e^(-u) / x!
where
u = the mean number of successes = 0.03
x = the number of successes = 1
Thus, the probability is
P ( 1 ) = 0.029113366 [ANSWER]
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d)
Note that the probability of x successes out of n trials is
P(x) = u^x e^(-u) / x!
where
u = the mean number of successes = 0.03
x = the number of successes = 0
Thus, the probability is
P ( 0 ) = 0.970445534 [ANSWER]