14.1. Definitions and Basics

Try these first

1. 1.

   Define a discrete random variable with an example.

   Hint

   Think of something that can be counted.

2. 2.

   What is a joint probability distribution?

   Hint

   Consider how two dice rolls might relate.

3. 3.

   What is a random variable?

   Hint

   Remember the connection to probability outcomes.

4. 4.

   For discrete random variables, what must the joint pmf always satisfy?

   • Must be negative
   • Must equal to 2
   • Must sum up to 1

   Hint

   Think about the total probability.

5. 5.

   Given a joint pmf for two discrete random variables X and Y, calculate the marginal pmfs and check independence from the provided joint distribution.

   Hint

   Look for the sums to equal 1 and the independence equalities.

6. 6.

   We have X ~ N(0, σ²) and Y ~ N(0, σ²) as jointly normal random variables. Show that X and Y being uncorrelated implies independence.

   Hint

   Remember the special properties of the normal distribution.