Practice Mathematical Conditions for Independence - 17.4 | 17. Independence of Random Variables | Mathematics - iii (Differential Calculus) - Vol 3
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17.4 - Mathematical Conditions for Independence

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the mathematical condition for independence between two discrete random variables?

💡 Hint: Look at the relationship between joint and marginal probabilities.

Question 2

Easy

How do we express independence in continuous random variables?

💡 Hint: Focus on how we relate joint PDF to marginal PDFs.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

Which of the following is TRUE for independent random variables?

  • P(X
  • Y) = P(X) + P(Y)
  • P(X
  • Y) = P(X) * P(Y)
  • f(x
  • y) = f(x) + f(y)

💡 Hint: Think about what independence mathematically implies.

Question 2

True or False: If two random variables are independent, their covariance is always zero.

  • True
  • False

💡 Hint: Consider how correlation and independence relate.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

A joint PMF of two discrete variables X and Y is provided. Calculate the marginal distributions and test if X and Y are independent. If X has values 1, 2 with corresponding probabilities, and Y has values 3, 4, write out the joint PMF table.

💡 Hint: Don't forget to sum across both variables carefully.

Question 2

Given a continuous joint PDF f(x, y) = xy for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1, derive the individual PDFs and check independence.

💡 Hint: Set up correct limits for integration and pay attention to normalization.

Challenge and get performance evaluation