Question

P(x) = (u^x. e^-u) / x! and let u=10. Find P(9).

Answer 1

$$P(x) = \dfrac{u^x e^{-u}}{x!}\\$$

at u = 10 and x =9

$$P(9) = \dfrac{10^{9} \times e^{-10}}{9!}\\ = \dfrac{10^{9} }{9! \times e^{10}}\\ = \dfrac{10^{9} }{362880 \times 22026.47}\\ = \dfrac{10^{9} }{7992965433.6} = \dfrac{1000000000 }{7992965433.6}\\ \simeq 0.12511 \\\implies 125.11 \times 10^{-3}$$