15.8. Independence and Marginals

Try these first

1. 1.

   Define independence between two random variables.

   Hint

   Think of how one variable's value affects another.

2. 2.

   What is a marginal distribution?

   Hint

   Consider how to isolate one variable from a joint distribution.

3. 3.

   What does it mean for two variables to be independent?

   • They are always the same
   • Knowing one gives no information about the other
   • They depend on each other

   Hint

   Recall the definition of independence.

4. 4.

   If f(x, y) = f(x) * f(y), what does that indicate?

   • True
   • False

   Hint

   Look at the properties of joint distributions.

5. 5.

   You have two random variables: X, representing the time taken to finish a project, and Y, representing the number of meetings held. If their joint pdf is given, explain how you would prove or disprove their independence.

   Hint

   Focus on how the integration works.

6. 6.

   A communication engineer observes that signal strength and background noise behave independently based on their joint distribution. Describe the analysis process using independence.

   Hint

   What do you compare to check independence?