The number of casualties experienced by a deep draft marine

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?

Solution

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]