Practice Concept of Joint Probability Distributions - 15.1 | 15. Marginal Distributions | Mathematics - iii (Differential Calculus) - Vol 3
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Knowledge

15.1 - Concept of Joint Probability Distributions

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is a joint probability density function?

💡 Hint: Think about how we measure the partnership of two events.

Question 2

Easy

How do we derive a marginal distribution?

💡 Hint: Consider what happens when you ignore one of the variables.

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 joint pdf represent?

  • Probability of individual variables
  • Probability of two variables occurring together
  • Probability of any random event

💡 Hint: Think about the definition of joint probabilities.

Question 2

True or False: Marginal distributions can be obtained from joint distributions.

  • True
  • False

💡 Hint: Consider how you isolate one variable from the others.

Solve and get performance evaluation

Challenge Problems

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.

💡 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.

💡 Hint: Consider how to apply convolution for deriving the distribution.

Challenge and get performance evaluation