Select each of the options below that are sufficient for theta. I have solved the problem. I just need all the correct answers that apply.

11. Let X1, X2, ..., Xn be independent identically distributed random variables with density function h(t; 0) = 0 , if t = [0, 1] 0+0-1, if te [0, 1]. Find a sufficient statistic for 0. Select each of the options below that are sufficient for theta. O The product of the observed values O All of the observed values except the last; and the mean of the observed values O The sum of the observed values The product of the logs of the observed values O The sum of the logs of the observed values