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

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What does PDF stand for?

πŸ’‘ Hint: Recall the acronym we discussed.

Question 2

Easy

What property ensures the area under a PDF equals one?

πŸ’‘ Hint: Think about the key requirements of a PDF.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

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

πŸ’‘ Hint: Consider what makes a valid probability distribution.

Question 2

Is the mean of a random variable always zero?

  • True
  • False

πŸ’‘ Hint: Think about different types of distributions.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

πŸ’‘ Hint: Refer to integration techniques for polynomials.

Question 2

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

πŸ’‘ Hint: Distributing and integrating will be key here.

Challenge and get performance evaluation