1. ## probability of breakdowns

Assuming that number of breakdowns per hour follows a poisson distribution with mean ( 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.

2. Originally Posted by Suchy
Assuming that number of breakdowns per hour follows a poisson distribution with mean ( λ) equal 0,4 answer the following:
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?.

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

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

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

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