The number of accidents occuring in a factory in a week is a

The number of accidents occuring in a factory in a week is a Poisson random variable with mean 3. The number of individuals injured in each accident are independent indentically random variables, each having a Poisson distribution with mean 2. In addition they are independent on the number of accidents.

(a) Determine the mean and the variance of the number of individuals injured in a week?

(b) Determine the average time of occurrence of the 3rd accident.

Solution

a)

mean and the variance in a poisson distribution is the same

mean = variance = landha = 2*3 = 6

b)

in the third accidents

3*3*3 = 27