Water in a reservoir is contaminated with disease causing ba

Water in a reservoir is contaminated with disease causing bacteria which occur (following a Poisson Process) with a mean rate of 2 per 10 liters. If you drink a liter of water per day, what is the probability that you will swallow at least one bacteria in one week?

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

reservoir is contaminated with disease causing bacteria which occur (following a Poisson Process) with a mean rate of 2 per 10 liters

Drink a liter of water per day for a week, mean rate = 7*2/10 = 1.4

P( X < 1) = P(X=0)   
= e^-1.4 * 2 ^ 0 / 0!   
= 0.2466

P( X > = 1 ) = 1 - P (X < 1) = 0.7534