One of the four gas stations located at an intersection of...

One of the four gas stations located at an intersection of two major roads is a Texaco station. Suppose the next six cars that stop at any of these four gas stations make their selections randomly and independently. Let $x$ be the number of cars in these six that stop at the Texaco station. Is $x$ a discrete or a continuous random variable? Explain.

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Key Concepts

Random Variable

A random variable is a numerical representation of the outcomes of a random process. It mathematically encapsulates the idea of randomness by assigning real numbers to outcomes of a probabilistic experiment, allowing for quantification and analysis of uncertainty.

Discrete Random Variable

A discrete random variable is one that takes on a countable number of distinct outcomes, often representing counts or enumerations. This type of variable is common in scenarios involving counting processes, where the possible outcomes are finite or countably infinite.

Continuous Random Variable

A continuous random variable, on the other hand, can assume any value within a given interval or continuum. It is used to model measurements and quantities that vary smoothly over a range, such as time or temperature, and its outcomes cannot be enumerated one by one.

Binomial Experiment

A binomial experiment refers to a statistical process that consists of a fixed number of independent trials, each with two potential outcomes (commonly labeled as 'success' or 'failure'), where the probability of success remains constant throughout the trials. It serves as a foundational model in situations where the number of successes in a given number of trials is counted.

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