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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the expectation of a random variable X uniformly distributed between 0 and 10?
💡 Hint: Use the formula for uniform distribution.
Question 2
Easy
How does expectation relate to the average value?
💡 Hint: Consider the definition of mean.
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 expectation E(X) for a continuous variable with pdf f(x)?
💡 Hint: Think about the integral definition related to area under a curve.
Question 2
True or False: The expectation of a random variable is always a value that the variable can take.
- True
- False
💡 Hint: Consider how averages can sometimes lie outside the original set, like for a uniform distribution.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider a continuous random variable X with pdf f(x) = 2x for 0 <= x <= 1. Calculate the expectation E(X) and interpret the result.
💡 Hint: Set up the integral carefully and bear in mind the function shape.
Question 2
A stock's price follows a normal distribution with a mean of $50 and standard deviation of $10. Calculate the expected price after 1 year assuming the same conditions hold.
💡 Hint: Consider why the mean value remains constant.
Challenge and get performance evaluation