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 count the num- ber of hearts.

Short answer

The described process is a discrete random variable.

Step-by-step solution

Understanding the nature of the event

Start by understanding what the event is asking of you. In this case, you are drawing 10 cards from a deck (which typically contains 52 cards) and counting the number of hearts. Any standard deck has 13 heart cards. You are drawing 10 cards, so the count of heart cards can be any number between 0 and 10 inclusive, depending on your draw.

Applying the basic concepts of Random Variables

Next, decide whether the outcome of the task corresponds to a random variable, and if so, what type of random variable it is. We know that a random variable is a numerical description of the outcome of a statistical experiment. A variable is defined as discrete if its possible values form a set of separate numbers, and as continuous if its possible values comprise an entire interval on the number line.

Identifying the type of Random Variable

Analyzing the stated event, count of hearts, can have only integer values from 0 to 10. This set of numbers are separate, thus it falls into the category of a discrete random variable.