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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define CDF and how it is used for continuous random variables.
💡 Hint: Think of how you define probabilities.
Question 2
Easy
What does it mean for a function to be non-decreasing?
💡 Hint: Consider how this looks on a graph.
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 main purpose of a CDF?
- To describe the probability of a variable being greater than a value
- To calculate the mean of a random variable
- To describe the probability of a variable being less than or equal to a value
💡 Hint: Think about what the CDF computes.
Question 2
Is the CDF for continuous variables a jump function?
- True
- False
💡 Hint: Consider the properties of continuous functions.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a continuous random variable with the PDF defined as f(x) = 6x(1-x) for x in [0,1], derive the CDF F(x).
💡 Hint: Use integration by parts or the power rule.
Question 2
Consider a random variable X with the CDF defined as F(x) = x^3 for x in [0,1]. What is its PDF?
💡 Hint: Recall the relationship between CDF and PDF.
Challenge and get performance evaluation