Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Fun, engaging games to boost memory, math fluency, typing speed, and English skillsβperfect for learners of all ages.
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a joint probability density function?
π‘ Hint: Think about how we measure the partnership of two events.
Question 2
Easy
How do we derive a marginal distribution?
π‘ Hint: Consider what happens when you ignore one of the variables.
Practice 4 more questions and get performance evaluation
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does the joint pdf represent?
π‘ Hint: Think about the definition of joint probabilities.
Question 2
True or False: Marginal distributions can be obtained from joint distributions.
π‘ Hint: Consider how you isolate one variable from the others.
Solve and get performance evaluation
Push your limits with challenges.
Question 1
Given two independent random variables with joint distribution defined as f(x,y) = 2xy for 0 < x < 1 and 0 < y < 1, find the marginal distributions, and verify their independence.
π‘ Hint: Use integration for marginals and confirm through multiplicative property.
Question 2
A random variable Z is defined as Z = X + Y, where X and Y are independent uniform random variables on [0, 1]. Determine the distribution of Z using joint distributions.
π‘ Hint: Consider how to apply convolution for deriving the distribution.
Challenge and get performance evaluation