Reading 3: Central Limit Theorem & Estimators

Reading 3: Central Limit Theorem & Estimators#

For the class on Wednesday, January 15th

Reading assignments#

  • Read the following sections of [WJ12] (sections based on the second edition)

    • Sec. 2.4.2.3 “Gaussian (Normal) distribution”

    • Sec. 3.2 “What should we expect of our statistics?”

  • (Optional) If you are adventurous, read the following sections of [Mur22] (sections based on the 2024-11-23 PDF file). These sections are a bit math-heavy, but they may give you a more concrete understanding of the concept of an estimator.

    • Sec. 5.3.1 “Computing the risk of an estimator”

    • Sec. 5.3.1.1 “Example”

Questions#

Submit your answer on Canvas. Due at noon, Wednesday, January 15th.

  1. List any concepts that confuse you from your reading. Explain why they confuse you. If nothing confuses you, briefly summarize what you have learned from this reading assignment.

  2. Use your own words to explain what an estimator is. Give one specific example of an estimator.

  3. I want to estimate the average enrollment of all the classes that are given at the U in Spring 2025. I uniformly at random choose \(N\) students at the U, ask each of them the average enrollment of all the classes that they are in, and then take the average of these numbers. Is this a consistent estimator? Is this an unbiased estimator? Why or why not?