Practice Variance and Relation to Expectation - 9.1.5 | 9. Expectation (Mean) | Mathematics - iii (Differential Calculus) - Vol 3
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Variance and Relation to Expectation

9.1.5 - Variance and Relation to Expectation

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Learning

Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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!

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