Reading 2: Summary Statistics

Reading 2: Summary Statistics#

For the class on Wednesday, January 15th

Reading assignments#

  • Read the following sections of [Mur22] (sections based on the 2024-11-23 PDF file)

    • Sec. 2.2.5 “Moments of a distribution”, and all of its subsections (2.2.5.1–2.2.5.4)

    • Sec. 2.2.6 “Limitations of summary statistics”

    • Sec. 3.1 “Joint distributions for multiple random variables”, and all of its subsections (3.1.1–3.1.5)

Questions#

Submit your answer on Canvas by noon, Wednesday, Jan 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. Sec. 2.2.5 of [Mur22] discusses the mean and variance of a distribution, and Sec. 2.2.6 mentions mean and variance of data points. These two concepts: summary statistics of a distribution (random variable) vs. summary statistics of data points (samples) are closely related but distinct in nature. Discuss how they differ using one example in physics, astronomy, or your field of study.

  3. Sec. 3.1.4 of [Mur22] discusses a few examples of spurious correlation due to hidden common causes. Try explaining this phenomenon using the concept of conditional independence (see Sec. 2.1.3.6 of [Mur22]).