Answer to Question #261901 in Statistics and Probability for Anjana

Question

The record of births, over the last 100 years maintained by the municipal council of a town showed that 200 children were born blind during that period. On the assumption that the number of children born blind in an year follows Poisson distribution, estimate the number of years in which there were (a) no blind births (b) one blind birth (c) two blind births 

Answer 1

Let $X=$ the number of births in year: $X\sim Po(\lambda)$

$$\lambda=200/100=2$$

(a)

$$P(X=0)=\dfrac{e^{-2}(2)^0}{0!}=e^{-2}\approx0.135335$$

$$0.135335(100)=14(years)$$

(b)

$$P(X=1)=\dfrac{e^{-2}(2)^1}{1!}=2e^{-2}\approx0.270671$$

$$0.270671(100)=27(years)$$

(c)

$$P(X=2)=\dfrac{e^{-2}(2)^2}{2!}=2e^{-2}\approx0.270671$$

$$0.270671(100)=27(years)$$