x equals

Part 1: Is $x$ a continuous or discrete random variable?

$x$ represents the number of questions a student answers correctly. Since the number of correct answers is counted in whole numbers (0, 1, 2, etc.), $x$ is a discrete random variable. A discrete variable takes on distinct, countable values.

So, $x$ is a discrete random variable.

Part 2: What are the possible values of $x$?

The number of correct answers can range from 0 (if the student answers no questions correctly) to 6 (if the student answers all questions correctly). Therefore, the possible values of $x$ are:

$x = \{ 0, 1, 2, 3, 4, 5, 6 \}$

Summary:

• a. $x$ is a discrete random variable.
• b. The possible values of $x$ are $\{ 0, 1, 2, 3, 4, 5, 6 \}$.

Do you want more details or have any questions?

Here are 5 related questions to expand on this:

1. What is the difference between continuous and discrete random variables?
2. How would you calculate the probability distribution of $x$?
3. Can you explain examples of continuous random variables in real life?
4. How would a binomial distribution apply to this problem?
5. What is the expected value of $x$ if each answer has a probability of 0.5 of being correct?

Tip: Discrete random variables are often used to model countable events like test scores, while continuous variables model measurable quantities like time or temperature.