1 / 7

Random Sampling

Random Sampling. Population Random sample: Independent variables Same probability distribution Statistics Point estimate. Examples. Mean of a single population Variance of a single population Difference in means of two population. Unbiasedness.

arvid
Download Presentation

Random Sampling

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Random Sampling • Population • Random sample: • Independent variables • Same probability distribution • Statistics • Point estimate

  2. Examples • Mean of a single population • Variance of a single population • Difference in means of two population

  3. 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() = .

  4. Example 1 • Given X = (5.8, 4.4, 8.7, 7.6, 3.1) • The Sample Mean • The Sample Median • The 20% trimmed mean

  5. Example 2 • Sample Variance • Expectation of Sample Variance

  6. 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 and variance , then the sample mean is the MVUE for

  7. Example 1 (continued)

More Related