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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a continuous random variable?
💡 Hint: Think of examples like temperature or time.
Question 2
Easy
Which function represents the probability of a continuous RV?
💡 Hint: Remember, it's a curve that describes probabilities.
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 primary purpose of a probability density function?
- To provide a list of probabilities
- To describe densities over intervals
- To show discrete outcomes
💡 Hint: Think about what a PDF represents graphically.
Question 2
The cumulative distribution function ranges from:
- -∞ to +∞
- 0 to 1
- 0 to ∞
💡 Hint: Consider how probabilities are represented in total.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the PDF f(x) = 6x(1-x) for 0 ≤ x ≤ 1, calculate the expectation value E(X) and the variance Var(X).
💡 Hint: First find the integral for E(X), then use the result to find Var(X).
Question 2
If a continuous random variable has a CDF F(x) = x^3 for 0 ≤ x ≤ 1, find the PDF and verify it integrates to 1.
💡 Hint: Differentiate the CDF to find the PDF, then integrate.
Challenge and get performance evaluation