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Inference About Independence

In this chapter, we will address the two following questions:

  • How do we test if two random variables are independent?
  • How do we estimate the strength of dependence between two random variables?

One should note that dependence and causation are two different things.

Example: A researcher found a very strong dependence between ice cream sales and robberies. It turned out that both events are triggered by hot temperatures. When weather is hot, people leave their homes to go to the beach more frequently.  But neither buying an ice cream triggers a robbery, nor a robbery triggers an ice cream sale.

Example: There is a strong dependence between football season and soft-drink sales. With

We write $Y \prod Z$ to indicate that $Y$ and $Z$ are independent.