7.5 - Probability Calculation
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Practice Questions
Test your understanding with targeted questions
What does PDF stand for?
💡 Hint: Recall the acronym we discussed.
What property ensures the area under a PDF equals one?
💡 Hint: Think about the key requirements of a PDF.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What property must a PDF satisfy?
💡 Hint: Consider what makes a valid probability distribution.
Is the mean of a random variable always zero?
💡 Hint: Think about different types of distributions.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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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