Practice Examples (17.5) - Independence of Random Variables - Mathematics - iii (Differential Calculus) - Vol 3

Practice: Examples

Lesson 17.5Independence of Random Variables

Practise this section

9 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What does it mean for random variables to be independent?
Show hintHide hint
Think of the dice examples we discussed.
Question 2.
How is the joint PMF represented for discrete random variables?
Show hintHide hint
Refer to the table format presented in our example.
3Question 3.
What indicates that two random variables are independent?
- P(X,Y) = P(X) * P(Y)
- P(X,Y) < P(X) * P(Y)
- P(X,Y) > P(X) * P(Y)
Show hintHide hint
Anchor this to the conditional probabilities we discussed.
4Question 4.
In discrete random variables, which function describes the joint probabilities?
- Marginal Probability Function
- Joint Probability Mass Function
- Mutual Information
Show hintHide hint
Check the terminology we used before.
Question 5.
Given X and Y with the joint PDF f(x,y) = e^(-x) * e^(-y), derive whether X and Y are independent.
Show hintHide hint
Calculate the marginal PDFs first.
Question 6.
Create a joint PMF for X and Y that showcases independence and calculate all relevant probabilities.
Show hintHide hint
Make sure distributions sum to 1 and check independence condition afterward.

5 more questions in this section. Enroll free to practise them all.