14. Partial Differential Equations

Try these first

1. 1.

   Define a discrete random variable.

   Hint

   Think of examples like the number of students in a classroom.

2. 2.

   What is a joint probability distribution?

   Hint

   Consider the outcomes of rolling two dice.

3. 3.

   What does a joint probability distribution measure?

   • Relationship between two variables
   • Variance of a variable
   • Sum of probabilities

   Hint

   Think about how different outcomes are connected.

4. 4.

   True or False: A joint PDF can be negative.

   • True
   • False

   Hint

   Consider the properties of probability distributions.

5. 5.

   Given a joint PDF f(x,y) = 3x^2y for 0 < x < 1, 0 < y < 1, calculate the marginal PDF of X.

   Hint

   Remember the integration limits and the formula!

6. 6.

   Two random variables are defined as independent if P(A and B) = ...? Fill in the blank.

   Hint

   Think about independence concepts!