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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the expected value of a continuous random variable with PDF f(x) = 3x² for x from 0 to 1?
💡 Hint: Use the integral definition of expected value.
Question 2
Easy
Define variance.
💡 Hint: Think about variability in data.
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 calculating the mean of a continuous random variable?
- E[X] = ∫ f(x) dx
- E[X] = ∫ x f(x) dx
- E[X] = ∫ (x - µ)² f(x) dx
💡 Hint: Focus on what you integrate.
Question 2
True or False: Variance can be zero for a random variable.
- True
- False
💡 Hint: Consider what variance measures.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A continuous random variable's PDF is given by f(x) = 12x(1-x) for 0 ≤ x ≤ 1. Calculate the mean and variance.
💡 Hint: Calculate the mean first and then use it to find the variance.
Question 2
For a normal distribution with mean 5 and standard deviation 2, determine E[X²] and its relationship to the variance.
💡 Hint: Recall the formulas relating mean and variance.
Challenge and get performance evaluation