1. Properties of Estimators Statistics: 1.Sufficiency 2.Un-biased 3.Resistance 4.Efficiency Parameters:Describe the population Describe samples. But we use it to estimate population parameters

2. Sample Variance as an Unbiased estimator Biased UNbiased Example population: y: 1, 2, 3

3. Samples of Two from the above population If Sample y: 1, 2 If

4. n versus n-1: All permutations SamplemeanVar(n)Var(n-1) 1,11.000 1,21.5.25.50 1,32.01.02.0 2,11.5.25.50 2,22.000 2,32.5.25.50 3,12.01.02.0 3,22.5.25.50 3,33.000 E=2.0.333.667

5. Not all n-1 estimates are “better” than their n counterparts. But, on average, n-1 is superior (Unbiased). Remember E = expected value Degrees of Freedom