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Knowledge
Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the expectation of a fair 6-sided die?
💡 Hint: Add the outcomes and divide by the number of faces.
Question 2
Easy
How do you define variance?
💡 Hint: Think about how far each value is from the average.
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
What is the formula for variance?
- E[X²] - (E[X])²
- E[X] - E[X²]
- E[X²] + E[X]
💡 Hint: Recall the definitions of expectation and variance.
Question 2
True or False: Variance measures how concentrated the mean is.
- True
- False
💡 Hint: Think about what variance represents.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A random variable X takes values 1, 2, 3 with probabilities 0.2, 0.5, 0.3. Calculate Var(X).
💡 Hint: Use the probabilities to find E(X) and E(X²) first.
Question 2
Explain how variance plays a role in the context of stochastic PDEs and provide a specific example.
💡 Hint: Link variance with real-life applications in PDEs!
Challenge and get performance evaluation