8 Consider a random sample X1, …, Xn from a Poisson distribution with expectation E[Xi ] = λ. An estimator ˆ λ for the parameter λ is given by the observed mean of the sample, that is: 1 1 ˆ n i i X n = λ = ∑ (ii) Calculate the exact probability that 0.2 ≤ ˆ λ ≤ 0.3 if the sample size is n = 10. In the solution to the above question, it is P[0.2<= lambda<=0.3] = P[2<= 10Lambda <=3) = { F[3; Lambda = 2.5] - F[1; Lambda = 2.5] Please explain why it is F[1] instead of F[2]?
