14.2.1. For Discrete Random Variables

Try these first

1. 1.

   What does the joint pmf for two discrete random variables provide?

   Hint

   Consider what 'joint' means in the context of probability.

2. 2.

   Write the first property of joint probability distributions.

   Hint

   Think about what probabilities should always be.

3. 3.

   What does a joint probability mass function describe?

   • The probability of one random variable
   • The combined probability of two discrete random variables
   • The area under a curve

   Hint

   Focus on 'joint' – it's about combinations.

4. 4.

   True or False: A joint pmf must always yield a negative probability.

   • True
   • False

   Hint

   Probabilities should not dip below zero!

5. 5.

   Suppose you have a joint pmf with P(X=0, Y=1) = 0.3 and P(X=0, Y=2) = 0.2. Calculate the marginal pmf for P(X=0).

   Hint

   Total all probabilities corresponding to X=0.

6. 6.

   Given a joint pmf indicating the failure rate of two machines X and Y is connected, show if they are independent or not, and explain why.

   Hint

   Independence means multiplication of individual probabilities works every time!