Let’s examine each item to determine the type of random variable (discrete, continuous, or not a random variable):

1. a. Responses to the survey question "Do you have children?"

   • The responses are categorical (yes or no).
   • This is not a random variable because it's a categorical response with no numerical value associated.

2. b. Shoe sizes (e.g., 8 or 8½) of humans

   • Shoe sizes are specific, countable values and are typically considered discrete random variables since they take on specific numbers or half-numbers.

3. c. Exact head circumference of human infants

   • Head circumference is a continuous measurement as it can take on any value within a range.
   • This is a continuous random variable.

4. d. Exact weights of the next 500 babies born in a region

   • Weight is also continuous because it can take on any value within a range.
   • This is a continuous random variable.

5. e. Number of pets in households

   • The number of pets is countable (0, 1, 2, etc.).
   • This is a discrete random variable.

Summary of Answers:

• a. Not a random variable
• b. Discrete random variable
• c. Continuous random variable
• d. Continuous random variable
• e. Discrete random variable

Would you like more details on each type of variable or have any questions?

Further Questions to Consider:

1. What differentiates a discrete random variable from a continuous random variable?
2. Can categorical responses ever be treated as a random variable in some contexts?
3. How do we model continuous random variables in statistical analysis?
4. Why are measurements like head circumference considered continuous?
5. What are some real-world applications of discrete random variables?

Tip:

A discrete random variable takes on countable values (like shoe sizes or the number of pets), while a continuous random variable takes on any value within a range (like weight or circumference).