Question

In Exercises \(\mathrm{P} .63\) to \(\mathrm{P} .67,\) state whether the process described is a discrete random variable, is a continuous random variable, or is not a random variable. Draw 10 cards from a deck and find the proportion that are hearts.

Short answer

The process describes a discrete random variable.

Step-by-step solution

Understanding Types of Variables

Discrete random variables have specific and countable outcomes, usually described as having a finite or countable number of outcomes. Continuous random variables, on the other hand, can take on any values in a given range and are usually measurements. Non-random variables are those that are not influenced by randomness.

Analyze Given Process

The process is about drawing 10 cards from a deck and finding the proportion of those cards that are hearts. This process has a countable number of outcomes since a deck of cards has a finite number of heart cards. The result, which is the proportion of heart cards, can only take certain values given a finite number of draws (i.e., 10 draws).

Identify the Type of Variable

Based on the analysis in Step 2, the process describes a discrete random variable. This is because the outcomes (i.e., the number of heart cards in 10 draws) are countable and finite.