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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the marginal PDF of X if the joint PDF is f(x,y) = 6xy for 0 ≤ x, y ≤ 1?
💡 Hint: Integrate 6xy with respect to y from 0 to 1.
Question 2
Easy
State the condition for marginal PDFs in relation to joint PDFs.
💡 Hint: Consider the definition of probability density functions.
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 marginal PDF represent?
- The probability distribution of multiple variables
- The distribution of a single variable from a joint distribution
- The cumulative distribution function
💡 Hint: Think about the term 'marginal' and its meaning in statistics.
Question 2
Integration is used to find marginal PDFs because it allows for:
- True
- False
💡 Hint: Recall the purpose of integration in mathematics.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the joint probability density function f(x,y) = 3x^2y for 0<x<1 and 0<y<1, derive f_X(x) and f_Y(y).
💡 Hint: Check your limits and ensure proper integration across defined boundaries.
Question 2
A researcher calculates the marginal PDF of X as f_X(x)=x^2 for x≥0. If the joint PDF integrates to 1, what does it indicate about Y?
💡 Hint: Remember that joint distributions always require summation to 1 across all dimensions.
Challenge and get performance evaluation