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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define Conditional PDF in your own words.
💡 Hint: Think about how one variable's understanding depends on another.
Question 2
Easy
What is the formula for Conditional PDF?
💡 Hint: Recall the relationship between joint and marginal PDFs.
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 Conditional PDF?
- f_{X,Y}(x,y) / f_Y(y)
- f_Y(y) / f_{X,Y}(x,y)
- f_{X,Y}(x,y) + f_Y(y)
💡 Hint: Consider the relationship defined by ratios.
Question 2
True or False: Conditional PDF can be interpreted as the ratio of joint PDF to marginal PDF.
- True
- False
💡 Hint: Remember the definition of Conditional PDFs.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given two independent random variables X and Y, explain how their independence affects their conditional densities.
💡 Hint: Think about the implications of independence in probability.
Question 2
A random variable has a joint PDF defined by f_{X,Y}(x,y) = 3x^2y for 0 < x < 1 and 0 < y < 1. Calculate the Conditional PDF f_{X|Y}(x|y).
💡 Hint: Start by finding the marginal function before approaching the conditional PDF.
Challenge and get performance evaluation