Practice Probability Calculation - 7.5 | 7. Probability Distribution Function (PDF) | Mathematics - iii (Differential Calculus) - Vol 3
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Probability Calculation

7.5 - Probability Calculation

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does PDF stand for?

💡 Hint: Recall the acronym we discussed.

Question 2 Easy

What property ensures the area under a PDF equals one?

💡 Hint: Think about the key requirements of a PDF.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What property must a PDF satisfy?

It can be negative
The total area under the curve is 0
The total area under the curve is 1

💡 Hint: Consider what makes a valid probability distribution.

Question 2

Is the mean of a random variable always zero?

True
False

💡 Hint: Think about different types of distributions.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given a continuous random variable with PDF f(x) = 12x(1-x) for 0 ≤ x ≤ 1, find the probability that X falls between 0.25 and 0.75.

💡 Hint: Refer to integration techniques for polynomials.

Challenge 2 Hard

Calculate the expected value (mean) of X when its PDF is given as f(x) = 6x(1-x) for 0 ≤ x ≤ 1.

💡 Hint: Distributing and integrating will be key here.

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