Question

How to tell the difference between discrete or continuous random variables given the weight of bags of apples, with 20 apples in a bag?

Answer 1

Answer: Continuous.

The primary difference between a discrete and a continuous random variable is that a continuous random variable can take on any value within a given range, while a discrete random variable is more limited. In the question provided, assuming that any given bag of apples will weigh between 5 and 25 pounds, a bag could weigh 5 pounds; it could also weigh 5.01 pounds, or 5.001 pounds, or 5.0001 pounds, etc. Within this finite range, the variable can take on an infinite number of values.

By contrast, an example of a discrete random variable might be the number of heads after `n` flips of a coin. In this case, our random variable could take on any whole number value between `0` and `n`, but could not take on a value of `0.1, 0.2, 0.5,` because we cannot flip a coin and get only a tenth, a fifth, or a half of a head. This random variable would be discrete, because it is not able to take on any arbitrary value within its range.

(Note that, even if we were counting the number of heads as `n->oo`, this would remain a discrete variable. In this case, our number of heads is said to be countably infinite. )