Random Variables and Distribution Workshop

Retrieval Prompts

1. Define a random variable without using the phrase "random number."
2. State what a PMF describes.
3. State what a CDF describes.
4. List the signature stories for binomial, hypergeometric, geometric, and Poisson models.

Compare and Distinguish

Separate these pairs clearly:

• event versus random variable
• PMF versus CDF
• binomial versus hypergeometric
• geometric versus binomial

Common Mistake Check

For each statement, identify the error:

1. "A random variable is just the event written with a capital letter."
2. "Sampling without replacement from a finite deck is binomial because there are only two outcomes."
3. "P(X <= 3) is the same thing as P(X = 3) if the support is discrete."
4. "The Poisson model is correct whenever the answer is a count."

Mini Application

For each scenario:

1. define a useful random variable
2. choose a plausible distribution family or explain why none of the core families fit directly
3. identify whether PMF or CDF language is more natural

Scenarios:

1. number of defects in a sample of 12 parts drawn from a lot with known defect count
2. number of successful logins among 30 independent attempts
3. number of requests until the first timeout
4. number of support tickets arriving in one hour

Evidence Check

This page is complete only if your variable definitions and model choices are justified in words, not just named.