14.1.2. Joint Probability Distribution

Try these first

1. 1.

   Define Joint PMF.

   Hint

   Think of it as the probability table for two variables.

2. 2.

   What do we call the probability of one variable independent of another?

   Hint

   Remember, it's about the influence of one on another.

3. 3.

   What does the joint PMF represent?

   • Probability of a single variable
   • Probability of multiple variables
   • Cumulative probability

   Hint

   Focus on the word 'joint'.

4. 4.

   True or False: If two random variables are independent, P(X, Y) = P(X) * P(Y).

   • True
   • False

   Hint

   Think about their interaction.

5. 5.

   Given a joint PMF where P(X=1, Y=0) = 0.2, P(X=1, Y=1) = 0.3, and all others are 0, compute marginal PMFs for X and Y.

   Hint

   Look carefully at how you sum probabilities.

6. 6.

   Consider a joint PDF f(x,y) = 2xy for 0 <= x <= 1 and 0 <= y <= 1. Confirm it is a valid PDF and find marginal PDFs for each variable.

   Hint

   Check for area under the curve.