Practice Independence Of Random Variables (17.3) - Independence of Random Variables

Practice: Independence of Random Variables

Lesson 17.3Independence of Random Variables

Practise this section

8 questions

Flashcard drill
2 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
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is a random variable?
Show hintHide hint
Think of what you measure in experiments.
Question 2.
Can independent random variables affect each other's outcomes?
Show hintHide hint
Reflect on the concept of independence.
3Question 3.
Two random variables are independent if:
- A) They have the same marginal distribution
- B) P(X = x
- Y = y) = P(X = x)P(Y = y)
- C) Cov(X
- Y) = 0
Show hintHide hint
Recall the definition of independence.
4Question 4.
If Cov(X, Y) = 0, then X and Y are definitely independent.
Show hintHide hint
Consider examples of uncorrelated but dependent variables.
Question 5.
Two people flip a coin simultaneously. Let A be the event of 'Person 1 gets heads' and B be 'Person 2 gets heads'. Are the events A and B independent? Justify your answer with probabilities.
Show hintHide hint
Consider the outcomes of independent events.
Question 6.
Given two dice rolls defined as random variables X and Y, show whether they are independent if the results are analyzed via conditional probabilities.
Show hintHide hint
Think about how the outcome of each die is calculated.

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