Assume a Poisson distribution with 58 Find the following pro

Assume a Poisson distribution with

=5.8

Find the following probabilities.

X=1

X<1

X>1

X1

Solution

a)

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 =    5.8      
          
x = the number of successes =    1      
          
Thus, the probability is          
          
P (    1   ) =    0.017559818 [ANSWER]

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b)

P(x<1) = P(0)

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 =    5.8      
          
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.003027555 [ANSWER]

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C)

Note that P(more than x) = 1 - P(at most x).          
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    5.8      
          
x = our critical value of successes =    1      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   1   ) =    0.020587372
          
Thus, the probability of at least   2   successes is  
          
P(more than   1   ) =    0.979412628 [answer]

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d)

Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    5.8      
          
x = the maximum number of successes =    1      
          
Then the cumulative probability is          
          
P(at most   1   ) =    0.020587372 [ANSWER]