Question

Decide whether a discrete or continuous random variable is the best model for each of the following variables. a) The number of times a transistor in a computer memory changes state in a time interval. b) The strength of concrete specimen. c) The number of convenience options selected by an automobile buyer d) The concentration of organic solids in a water sample. e) The weight of an injection molded plastic part.

Answer 1

Discrete random variables are used for countable instances while continuous random variables are for measurable quantities. The number of transistor state changes and the number of automobile options selected are discrete, while the strength of concrete, concentration of organic solids, and weight of a plastic part are continuous.

Step-by-step explanation:

When deciding whether a random variable is discrete or continuous, we consider if the variable is countable or measurable. Let's analyze each scenario provided:

• Discrete random variable for the number of times a transistor changes state as it is a countable instance.
• Continuous random variable for the strength of concrete specimen as strength is measured.
• Discrete random variable for the number of convenience options selected by an automobile buyer since options are counted.
• Continuous random variable for the concentration of organic solids in a water sample, as concentration is measured.
• Continuous random variable for the weight of an injection molded plastic part because weight is measured.

For discrete random variables, probabilities must be between zero and one, and their sum should be one. Continuous random variables can assume any value within an interval and are often used in fields like reliability and analytics.