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Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the expectation of rolling a fair 4-sided die?
💡 Hint: Use the formula for discrete expectations.
Question 2
Easy
Find the expectation of the number of heads in two tosses of a fair coin.
💡 Hint: List down the possible outcomes.
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 does the Expectation of a random variable represent?
- A frequency
- An average value
- A probability
💡 Hint: Consider what we mean by the 'long-run average'.
Question 2
True or False: The expectation of a constant is always equal to the constant itself.
- True
- False
💡 Hint: Review the properties of expectation.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Let X be the number of defective items in a sample of size n. Given a fixed probability p, formulate E(X) in a binomial context.
💡 Hint: Refer back to the binomial expectations formula!
Question 2
In a stochastic system, develop a PDE using E[u(x, t)] and show how it simplifies to a deterministic equation.
💡 Hint: Think about how taking averages can smooth out variability.
Challenge and get performance evaluation