Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Random Sampling Population Random sample: Independent variables Same probability distribution Statistics Point estimate 1 Examples Mean of a single population 2 Variance of a single population Difference in means of two population 1 2 2 Unbiasedness An estimator of some unknown quantity is said to be unbiased if the procedure that yields has the property that, were it used repeatedly the long-term average of these estimates would be . That is to say, E() = . 3 Example 1 Given X = (5.8, 4.4, 8.7, 7.6, 3.1) The Sample Mean X ~ The Sample Median X The 20% trimmed mean Xtr ( 20) 4 Example 2 Sample Variance n S2 2 ( X X ) i i 1 n 1 Expectation of Sample Variance E(S ) 2 2 5 Variance of a Point Estimator MVUE – Smallest variance estimator Theorem If X1,…Xn is a random sample of size n form a normal distribution with mean 2 and variance , then the sample mean X is the MVUE for 6 Example 1 V( X) (continued) 2 n ~ 2 V ( X) V( Xtr ( 20) ) 2 0.6n 7