The mode of a discrete random variable X with probability distribution p(x) is that value Xm for which p(x) is largest (ie Xm is the most probable x value). Let X ~ Poisson(λ) .
i) By considering the ratio P(X = x+1) / P(X=x) show that the mode of the Poisson distribution if the largest integer less than λ.
ii) Explanin what happens to the mode if λ is an integer value?