probability of breakdowns

May 2010
9
0
Assuming that number of breakdowns per hour follows a poisson distribution with mean ( [FONT=&quot]λ) equal 0,4 answer the following:
a) calculate the probability that the peeler does not have any breakdowns within an hour.
b) calculate the probability that a maximum of 1 breakdown happens within 8 hours.
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galactus

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Assuming that number of breakdowns per hour follows a poisson distribution with mean ( [FONT=&quot]λ) equal 0,4 answer the following:[/FONT]
Is it safe to assume that 0,4 means 0.4?. Are you in one of those countries where they use a comma for a decimal point?. (Lipssealed)

\(\displaystyle f(x;{\lambda})=\frac{{\lambda}^{x}e^{-\lambda}}{x!}\)

a) calculate the probability that the peeler does not have any breakdowns within an hour.
In the above formula, x=0. So, we have
\(\displaystyle f(0;0.4)=\frac{{\lambda}^{0} e^{-0.4}}{0!}\)

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b) calculate the probability that a maximum of 1 breakdown happens within 8 hours.
[/FONT]\(\displaystyle {\lambda}=(0.4)(8)=3.2\)

\(\displaystyle f(\text{at most 1}; 3.2)=\frac{(3.2)^{0}e^{-3.2}}{0!}+\frac{(3.2)^{1}e^{-3.2}}{1!}\)
 
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