Practice Continuous Random Variables - 8.2.2 | 8. Cumulative Distribution Function (CDF) | Mathematics - iii (Differential Calculus) - Vol 3
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Continuous Random Variables

8.2.2 - Continuous Random Variables

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define CDF and how it is used for continuous random variables.

💡 Hint: Think of how you define probabilities.

Question 2 Easy

What does it mean for a function to be non-decreasing?

💡 Hint: Consider how this looks on a graph.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the main purpose of a CDF?

To describe the probability of a variable being greater than a value
To calculate the mean of a random variable
To describe the probability of a variable being less than or equal to a value

💡 Hint: Think about what the CDF computes.

Question 2

Is the CDF for continuous variables a jump function?

True
False

💡 Hint: Consider the properties of continuous functions.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given a continuous random variable with the PDF defined as f(x) = 6x(1-x) for x in [0,1], derive the CDF F(x).

💡 Hint: Use integration by parts or the power rule.

Challenge 2 Hard

Consider a random variable X with the CDF defined as F(x) = x^3 for x in [0,1]. What is its PDF?

💡 Hint: Recall the relationship between CDF and PDF.

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