Practice Partial Differential Equations - 17 | 17. Independence of Random Variables | Mathematics - iii (Differential Calculus) - Vol 3
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Partial Differential Equations

17 - Partial Differential Equations

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define a random variable.

💡 Hint: Think about the outcomes of a certain experiment.

Question 2 Easy

What does a Probability Mass Function (PMF) describe?

💡 Hint: What type of variable is countable?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the definition of independent random variables?

They influence each other's distribution
They do not affect each other's probabilities
They must have the same mean

💡 Hint: Think about how one event might not influence another.

Question 2

For discrete variables, P(X=x, Y=y) = P(X=x) * P(Y=y) holds true if they are independent. True or False?

True
False

💡 Hint: Recall the definition you studied.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given a joint distribution P(X,Y) = P(X)P(Y) where P(X=1) = 0.5, P(Y=1)=0.4, find P(X=1, Y=1).

💡 Hint: Think about using the independence condition.

Challenge 2 Hard

Prove that two random variables are dependent if P(X=x,Y=y) does not equal P(X=x)P(Y=y).

💡 Hint: Consider cases where the multiplication law fails.

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