Practice Marginal Distributions - 14.3 | 14. Joint Probability Distributions | Mathematics - iii (Differential Calculus) - Vol 3
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14.3 - Marginal Distributions

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the formula for the marginal PMF of X in a discrete joint distribution?

💡 Hint: Think of summing over the probabilities in the joint PMF.

Question 2

Easy

In continuous distributions, what do we do to find the marginal PDF of X?

💡 Hint: Integration will help you collapse the other variable.

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 a marginal distribution refer to in probability theory?

  • The overall distribution of multiple variables
  • The distribution of a single variable
  • The joint distribution of two variables

💡 Hint: Focus on the term 'marginal' which indicates focusing on one aspect.

Question 2

True or False: Marginal distributions can only be derived from discrete random variables.

  • True
  • False

💡 Hint: Consider the definitions of marginals for different types of random variables.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

In a joint distribution of two dice rolls, what is the marginal distribution of one die? Provide a detailed explanation of your process.

💡 Hint: Start with a joint probability table, then aggregate relevant entries.

Question 2

Given a joint PDF of f(x,y) = 2x + 3y for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1, derive the marginal PDFs and verify if they support independence.

💡 Hint: Evaluate the integrals correctly and then set up their products.

Challenge and get performance evaluation