Leaks occur along a pipeline at the mean rate of 05 leaks pe

Leaks occur along a pipeline at the mean rate of 0.5 leaks per mile. Assume Poisson properties apply. What is te probability that a 3 mile stretch will have no leaks a .0498 b. .6065 c. 3679 d. .2231

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials

mean rate of 0.5 leaks per mile
For 3 Mile the mean rate be 0.5 * 3 = 1.5

P( 3 mile stretch will have no leaks) = P( X = 0 ) = e ^-1.5 * 1.5^0 / 0! = 0.2231