Question

question 2
match the two types of random variables with their definitions.
discrete random variable
choose
continuous random variable
choose
options:

• has a finite or countable number of possible outcomes that can be listed.
• has an uncountable number of possible outcomes, represented by an interval on the number line.

question 3
a discrete probability distribution must satisfy the following conditions:

1. the probability of each value of the discrete random variable is between select and select, inclusive.
2. the sum of all probabilities in a discrete probability distribution is select.

question 4
true or false. the expected value of a discrete random variable is equal to the mean of the random variable.
true
false

Explanation:

Match random variables with definitions

• Discrete Random Variable: Has a finite or countable number of possible outcomes that can be listed.
• Continuous Random Variable: Has an uncountable number of possible outcomes, represented by an interval on the number line.

Determine discrete probability distribution conditions

• Condition 1: The probability of each value of the discrete random variable is between 0 and 1, inclusive.
• Condition 2: The sum of all probabilities in a discrete probability distribution is 1.

Evaluate expected value statement

• The expected value \(E(X)\) of a discrete random variable is mathematically defined as the mean \(\mu\) of the random variable:

$$ E(X) = \mu = \sum x \cdot P(x) $$

• Therefore, the statement is True.

Answer:

Question 2

• Discrete Random Variable: Has a finite or countable number of possible outcomes that can be listed.
• Continuous Random Variable: Has an uncountable number of possible outcomes, represented by an interval on the number line.

Question 3

1. The probability of each value of the discrete random variable is between 0 and 1, inclusive.
2. The sum of all probabilities in a discrete probability distribution is 1.

Question 4

• True (Correct answer)
• False