Question

Let Y = the number of siblings for a student at a local high school. Suppose we choose someone from the school at random. The probability

distribution of Y is as follows.
Y
1
2
3
4
5+
0
0.02
Probability
0.25
0.35
0.20
0.10
0.08

Is Y a discrete or continuous? Explain.

Answer 1

Y is a discrete random variable because it represents countable numbers of siblings; its values are countable integers and the probability distribution for Y meets the criteria of being between zero and one and summing to one.

Step-by-step explanation:

The given variable Y, representing the number of siblings for a student at a local high school, is a discrete random variable. This is because the values that Y can take on are countable numbers of siblings, which include the integers 0, 1, 2, 3, and "5 or more" for those with five or more siblings.

Additionally, the probability distribution associated with Y meets the two essential characteristics of a discrete probability distribution function (PDF): each probability for a value of Y is between zero and one (inclusive), and the sum of all the probabilities adds up to one.

For example, the likelihood of a randomly selected student having one sibling is 0.25, two siblings is 0.35, and so forth. The probabilities of each possible outcome—in this case, the number of siblings—are given, and the scenario is regarding a finite count of individuals, not a continuous measurement. Hence, Y is discrete.

Understanding the difference between discrete and continuous random variables is important in probability and statistics as it dictates the type of probability distribution function used to represent the variable.