What is a random variable?

What is a random variable?

• A. It is constant across time.
• B. A random variable is one that varies over time or across observations.
• C. It is always normally distributed.
• D. It is the same as a fixed coefficient.

Answer: (B)

A random variable is a quantity whose value is determined by a random process and can take different values in different observations or over time. That variability is what makes it random—you don’t know the exact value until the outcome is observed. For example, rolling a six-sided die yields a random variable that can be 1 through 6, and across many trials you’ll see different results. This is why the description that it varies over time or across observations is the best choice. It isn’t required to be constant, since a true constant wouldn’t be random. It also isn’t required to be normally distributed; the distribution of a random variable depends on the process that generates it. And it isn’t the same as a fixed coefficient in a model, which is a constant parameter, whereas a random variable embodies randomness and can take on different values.

A random variable is a quantity whose value is determined by a random process and can take different values in different observations or over time. That variability is what makes it random—you don’t know the exact value until the outcome is observed. For example, rolling a six-sided die yields a random variable that can be 1 through 6, and across many trials you’ll see different results. This is why the description that it varies over time or across observations is the best choice.

It isn’t required to be constant, since a true constant wouldn’t be random. It also isn’t required to be normally distributed; the distribution of a random variable depends on the process that generates it. And it isn’t the same as a fixed coefficient in a model, which is a constant parameter, whereas a random variable embodies randomness and can take on different values.