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Reading 1: Probability and Random Variables

Reading 1: Probability and Random Variables#

For the class on Wednesday, January 10th

Reading assignments#

  1. Read the following sections of [Mur22] (sections based on the 2023-06-21 draft PDF file)

    • Sec. 2.1 “Introduction”, and all of its subsections (2.1.1–2.1.3.6)

    • Sec. 2.2 “Random variables”

    • Sec. 2.2.1 “Discrete random variables”

    • Sec. 2.2.2 “Continuous random variables”, and all of its subsections (2.2.2.1–2.2.2.3)

    • Sec. 2.2.3 “Sets of related random variables”

Questions#

Hint

Submit your answer on Canvas. Due at noon, Wednesday, Jan 10th.

  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.

Discussion Preview#

Note

We will discuss the following questions in class. They are included here so that you have a chance to think about them before class. You need not submit your answers as part of this assignment.

  1. Sec. 2.1.2 of [Mur22] discussed epistemic/model uncertainty and aleatoric/data uncertainty. In physics and astronomy, these two types of uncertainty are often referred to as systematic uncertainty and statistical uncertainty. The textbook mentioned an example of coin tossing. Give another example in physics and astronomy (or your field of study) to illustrate these two types of uncertainty.

  2. Consider the probability density function \(p(x)\) of a continuous random variable. If you know \(p(3) = 4\), how would you explain what this equation means for that random variable?

  3. In physics and astronomy, people often use statements such as “a \(3\sigma\) detection”. Based on what you read in Sec. 2.2.2.3 of [Mur22], how would you explain what “a \(3\sigma\) detection” means statistically?

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