Practice Properties of PDF - 7.2.4 | 7. Probability Distribution Function (PDF) | Mathematics - iii (Differential Calculus) - Vol 3
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Properties of PDF

7.2.4 - Properties of PDF

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Explain what non-negativity means in the context of PDFs.

💡 Hint: Think about the concept of probability.

Question 2 Easy

What is normalization of a PDF?

💡 Hint: Consider how probabilities should sum up.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does normalization ensure for a PDF?

Total probability equals zero
Total probability equals one
PDF values can be negative

💡 Hint: Remember that probabilities must always have a sum.

Question 2

True or False: The mean of a random variable gives us its most common value.

True
False

💡 Hint: Consider what average means versus frequency.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

If a PDF is given as f(x) = 1/2 for 0 ≤ x ≤ 2, calculate the mean and variance.

💡 Hint: You may use integration techniques.

Challenge 2 Hard

Find the probability that a random variable X, described by the PDF f(x) = 3x² for 0 ≤ x ≤ 1, lies between 0.5 and 1.

💡 Hint: Remember to set up your integral limits correctly.

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