Practice For Continuous Random Variables - 14.2.2 | 14. Joint Probability Distributions | Mathematics - iii (Differential Calculus) - Vol 3
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For Continuous Random Variables

14.2.2 - For Continuous Random Variables

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does the joint pdf represent for continuous variables?

💡 Hint: Think about how this relates to probabilities over an area.

Question 2 Easy

State one property of joint distributions for continuous random variables.

💡 Hint: Recall the implications of negative probabilities.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

Which of the following must always be true for a joint pdf?

It can be negative
The integral over the entire plane equals 1
It can vary significantly

💡 Hint: Consider why probabilities require summation to be meaningful.

Question 2

True or False: A joint pdf is always greater than or equal to zero.

True
False

💡 Hint: Reflect on the nature of probabilities.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given a joint pdf f(x,y) = Kxy for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1, find the value of K ensuring that the total probability is 1.

💡 Hint: Use double integration and the limits of x and y to find K.

Challenge 2 Hard

Create a joint probability distribution function for two variables, x and y, and verify its properties.

💡 Hint: Construct the joint pdf meaningfully based on real-world data or scenarios.

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