 So, discover minimal sufficient statistics we're going to look at the binomial distribution. As a consequence of Fisher's factorisation here we're really looking to see when if we have the ratio of the two PDFs or PMS when are they independent of my parameters of interest or constant with respect to that parameter. Ond mae wir i'r ystafell o'r dyfodol bynomial sy'n teimlo'i x, ystod yn y twelwch i ymwy. Rym ni'n credu i'r peryfoddau sy'n argynnau'r peromethau. Rydyn ni'n cael ei ddweudio'r gynllen o'r wych. Rydyn ni'n credu i'r ddweudio'r ddwyfoddau x, 1 minus tau to the n minus x over tau to the power of y, 1 minus tau to the power of n minus y. That's for single observation. For more than one observation and observations, we have tau to the power of the sum of xi, 1 minus tau n minus the sum of xi, tau to the power of the sum of yi, 1 minus tau to the power of n minus the sum yi. You can see this is constant with respect to our parameter tau here, if and only if the sum of xi is equal to the sum of yi. Also n minus the sum of xi is equal to n minus the sum yi as a consequence of this statement. So your minimal sufficient statistic is the sum of xi when you also need your n, of course.