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hello this is the next video in a playlist that im calling parameter estimation and were going to look at complete statistics so the definition is this let t be a statistic right its a function of our data with t following this distribution uh either continuous or discrete where the parameter theta lives in omega the the parameter space omega let that f so this density be in this family of distributions which is indexed by theta t is complete for family script f if the expected value of every function of our statistic equals zero and this for all theta implies that our function g of t is equal to zero for all theta and this is almost everywhere so if this is true but this is true except for like one point then its still true because that point has probability zero so the probability that g of t equals zero is one right because the probability of a point is zero so it doesnt play a part example one show that x n the nth order statistic is sufficient and complete when x i is from a
