Question

A hotel has two different ice machines that fill buckets of ice independently of each other. Let a represent the amount of ice in a bucket filled by machine a, and let b represent the amount of ice in a bucket filled by machine b. Which of the following choices explains the meaning of independent random variables in this context?

1) The independence of the two ice machines means that they fill buckets of ice approximately normally.
2) The independence of the two ice machines means that the two random variables have a correlation of 1.
3) The independence of the two ice machines means that knowing how much one machine fills does not help us predict how much the other fills.
4) The independence of the two ice machines means that if one machine is filling ice buckets properly, the other has a smaller probability of filling ice buckets properly.

Answer 1

The meaning of independent random variables in this context is that knowing how much one machine fills does not help us predict how much the other fills.

Step-by-step explanation:

The meaning of independent random variables in this context is that knowing how much one machine fills does not help us predict how much the other fills. In other words, the amount of ice filled by machine a does not depend on the amount of ice filled by machine b. The two ice machines are independent of each other, meaning they operate separately and their actions do not affect each other.