Question

For a certain type of copper wire, it is known that, on the average, 1.5 flaws occur per

millimeter. Assuming that the number of flaws is a Poisson random variable, what is

the mean number of flaws in a portion of length 5 millimeters? What is the

probability, in 4 significant figures, that no flaws occur in a certain portion of wire of

length 5 millimeters?

Answer 1

$X\sim Poiss\left( 1.5l \right) , l\,\,-\,\,length\,\,in\,\,mm\\X_5\sim Poiss\left( 1.5\cdot 5 \right) =Poiss\left( 7.5 \right) \\EX_5=7.5\\P\left( X_5=0 \right) =e^{-7.5}=0.0005531$