17.2. Joint Distribution of Random Variables

Try these first

1. 1.

   Define joint distribution and provide examples of its types.

   Hint

   Think about how we measure joint occurrences.

2. 2.

   State the formula for joint PMF.

   Hint

   Look at how we express probabilities for discrete cases.

3. 3.

   What does a joint distribution describe?

   • The distribution of a single variable
   • The relationship between two or more variables
   • The probability of a variable over time

   Hint

   Think about what relationships we study in statistics.

4. 4.

   True or False: Two independent random variables must have a joint distribution that equals the product of their marginal distributions.

   • True
   • False

   Hint

   Recall the independence formula discussed in class.

5. 5.

   Consider a joint PMF table for random variables X and Y:

   Y/X	1	2
   1	0.2	0.3
   2	0.1	0.4

   Check the independence of X and Y.

   Hint

   Look for any discrepancies between the joint PMF and the products of marginals.

6. 6.

   Given f(x,y) = xe^{-x}ye^{-y} for x,y>0, determine if X and Y are independent.

   Hint

   Verify by directly calculating the products of the marginals!