Practice Why Independence Matters in PDEs - 17.6 | 17. Independence of Random Variables | Mathematics - iii (Differential Calculus) - Vol 3
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17.6 - Why Independence Matters in PDEs

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the definition of independence in random variables?

💡 Hint: Think about the relationship between probabilities.

Question 2

Easy

Give an example of independent random variables in real life.

💡 Hint: Consider scenarios where one event does not influence the other.

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

If P(X=x, Y=y) = P(X=x) * P(Y=y), what can we say about X and Y?

  • They are dependent
  • They are independent
  • Not enough information

💡 Hint: Consider the implications of the joint probability.

Question 2

True or False: Independence of random variables means that their expected values can be treated independently.

  • True
  • False

💡 Hint: Think about how expected values are combined for independent variables.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Consider two continuous random variables X and Y with joint PDF f(x, y) = e^(-x) * e^(-y). Verify if they are independent.

💡 Hint: Look closely how you can factor the joint PDF.

Question 2

In a certain communication system, noise variables N1 and N2 are modeled as independent. If both have a mean of 0 and variance of 1, what can be said about their influence on the total noise N = N1 + N2?

💡 Hint: Remember the properties of independent random variables.

Challenge and get performance evaluation