Let X1 X2 be idd with distribution Poisson8 Prove that for

Let X1, X2, ... be i.d.d with distribution Poisson(8). Prove that for some n, we ahve P(X1+X2+...+Xn> 9n) < .001

we know that a poisson distribution with landha = 8

each variable have the same distribution with same landha

so if we sum all the landha

we will know that 8+8+8+8 = 8n

multiply by n because we dont know the number of landha

and 9n will have the same units

that probability will be less than 0.001

because X1+X2+...Xn will increase the variability of the distribution