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Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
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