17.2.1. Joint Probability Mass Function (PMF)

Try these first

1. 1.

   Define a Joint Probability Mass Function.

   Hint

   Think of it as a function relating two outcomes.

2. 2.

   Give an example of a discrete random variable.

   Hint

   Focus on countable outcomes.

3. 3.

   What does Joint PMF indicate?

   • Probability of single events
   • Joint likelihood of two events
   • Marginal distribution

   Hint

   Think about the combined outcomes.

4. 4.

   True or False: If two random variables are independent, their joint PMF can be expressed as the product of their individual PMFs.

   • True
   • False

   Hint

   Recall the independence formula we discussed.

5. 5.

   You are given a joint PMF where P(X=1, Y=1)=0.5, P(X=1, Y=2)=0.3, and P(X=2, Y=2)=0.2. Check if X and Y are independent.

   Hint

   Sum the probabilities to find marginal values first.

6. 6.

   You have P(X=1, Y=1)=0.25, P(X=1, Y=2)=0.25, P(X=2, Y=1)=0.25, P(X=2, Y=2)=0.25. Are X and Y independent?

   Hint

   This illustrates proper checking for equality in independence.