15.2. Definition of Marginal Distributions

Try these first

1. 1.

   Define marginal distribution in your own words.

   Hint

   Think about focusing on one variable only.

2. 2.

   What is the method to find the marginal pdf of X from the joint pdf?

   Hint

   Recall integration over the variable that is not of interest.

3. 3.

   What is the marginal distribution?

   • Only considers one variable.
   • Combines multiple distributions.
   • Focuses on joint probability.

   Hint

   Think of how you analyze one aspect at a time.

4. 4.

   True or False: The marginal distributions for continuous variables require summation.

   • True
   • False

   Hint

   Remember the method for continuous cases.

5. 5.

   Given a joint distribution f(x,y) = 12xy, 0 < x < 1, 0 < y < 1, find the marginal distributions for both X and Y.

   Hint

   Remember the limits set for x and y!

6. 6.

   Explain the significance of knowing if two random variables are independent in terms of marginal distributions.

   Hint

   Think about the relationship between independence and probabilities.