 So, here we're going to look at finding the minimal sufficient statistic for Poisson data. We start with recalling the results of Fischer's factorization theorem and basically we're going to look at the ratio of a Poisson distribution in terms of x and in terms of y and we're going to find out when they're independent of the parameter and the parameter that we'll be looking at in terms of a Poisson distribution is lambda. So, if we have our Poisson distribution here and we think about this and thus is in terms of x, so if we think about it as instead of one observation we have n observations, we would have our ratios would be e to the minus n lambda, lambda to the sum of xi over the product i equals 1 to n of xi factorial and this is it. And if we were looking at this in terms of the ratio between our x's and y's, we can do this in a single step, so we'd multiply this by the product of i equals 1 to n of yi factorial and we'll divide that by e to the minus n lambda over lambda to the sum of yi i equals 1 to n. The e to the power of n lambdas or minus n lambdas cancel each other out, so you get lambda to the power of the sum of xi minus the sum of yi and then you also have the product i equals 1 to n yi factorial divided by the product i equals 1 to n of xi factorial. Now this is constant with respect to lambda or independent of lambda if and only if these terms turn to zero. So we have independent of lambda if and only if the sum of xi is equal to the sum of yi so our minimal sufficient statistic for lambda equals the sum of your data.