Week 6 — Random Variables

Welcome to your Week 6 Start Here page.

Why this matters

An emergency-room nurse planning staff and a delivery driver planning a route both lean on two numbers you learn this week: an expected value and a standard deviation.

In plain language

Many numbers in daily life stay unknown until chance decides them, like the total on two dice or the weight of the next bird a field team catches. This week you treat such a number as a random variable (a number whose value a chance process sets). You list its possible values with their chances, which is its probability distribution (the full list of values and how likely each one is). Then you find its expected value (the average it settles toward over many tries) and its standard deviation (how far one result typically lands from that average). Last, you meet the density curve (a smooth curve whose area gives chances) for numbers such as weight that can take any value in a range.

• Already covered: Weeks 1 to 4 described data you already have; Week 5 measured chance with probability rules.
• This week: random variables, expected value, standard deviation, shifting and rescaling, and density curves.
• How they connect: Week 3's mean and SD now describe a chance process.
• Where we're going next: Week 7, Binomial & Normal Models, brings two ready-made distributions.

Focus

What is a chance-set number worth on average, and how far does one result swing?

By the end of this module, you should be able to:

• [ ] tell a discrete random variable from a continuous one
• [ ] check that a probability table is legitimate and read chances from it
• [ ] compute and interpret an expected value and a standard deviation
• [ ] predict what shifting and rescaling do to the mean and the standard deviation
• [ ] read probability as area under a density curve

To-do

Plan your week

1. Read Chapter 6 (about 45 minutes), then the lecture and slides.
2. Work the lecture tutorial (60–90 minutes) and the practice set (about 20 minutes).
3. Do the Data Lab (about 90 minutes), the discussion, and the assignment.
4. Take the quiz.

This week's checkpoint: compute E(X) = 3.5 for one fair die and explain why no single roll shows 3.5.

You've got this

Take it in order, and ask your instructor early if a step snags.

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