14.2. Properties of Joint Distributions

Try these first

1. 1.

   What does the term joint probability distribution refer to?

   Hint

   Think about how we describe events happening at the same time.

2. 2.

   True or False: In a joint distribution, probabilities can be negative.

   Hint

   Consider the properties of probabilities.

3. 3.

   What does the joint distribution of two random variables measure?

   • Their individual probabilities
   • Their combined probabilities
   • Their conditional probabilities

   Hint

   Consider what 'joint' implies.

4. 4.

   True or False: The total area under a joint PDF equals 1.

   • True
   • False

   Hint

   Think about the properties of how probabilities are represented.

5. 5.

   Consider three random variables: X, Y, and Z with a joint PMF defined at specific points. Demonstrate how to verify whether it's valid based on the non-negativity and normalization properties.

   Hint

   It's about verifying all conditions are met.

6. 6.

   A joint pdf is given as f(x,y) = Kxy for 0 < x < 1 and 0 < y < 1. Find the value of K for normalization.

   Hint

   Use double integration for continuous variables!