14.3.1. Marginal PMF (Discrete)

Try these first

1. 1.

   What is the formula for calculating the marginal PMF of variable X?

   Hint

   Think about how you want to isolate the variable X.

2. 2.

   Provide an example of a discrete random variable.

   Hint

   Consider discrete outcomes from an experiment.

3. 3.

   What is the marginal PMF of variable X?

   • Calculated by summing probabilities of the joint distribution for Y
   • Independently calculated from the other variables
   • Equal to the joint PMF of X

   Hint

   Remember the formula for marginal PMF!

4. 4.

   Marginal PMFs help in understanding the relationship between variables. True or False?

   • True
   • False

   Hint

   Reflect on the importance of isolating each variable.

5. 5.

   A joint PMF is defined as follows: $P(X=0, Y=0) = 0.1, P(X=0, Y=1) = 0.2, P(X=1, Y=0) = 0.3, P(X=1, Y=1) = 0.4$. If you add a new variable Z such that Z can take values 1 or 0, how does that affect the calculation of marginal PMFs for X?

   Hint

   Focus on how new variables interact with existing distributions.

6. 6.

   If two discrete random variables X and Y have identical marginal distributions but are dependent, provide a scenario in which this can occur.

   Hint

   Think about variables where one's outcome affects the other.