Practice Probability Calculation (7.5) - Probability Distribution Function (PDF)

Practise this section

9 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What does PDF stand for?
Show hintHide hint
Recall the acronym we discussed.
Question 2.
What property ensures the area under a PDF equals one?
Show hintHide hint
Think about the key requirements of a PDF.
3Question 3.
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
Show hintHide hint
Consider what makes a valid probability distribution.
4Question 4.
Is the mean of a random variable always zero?
- True
- False
Show hintHide hint
Think about different types of distributions.
Question 5.
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.
Show hintHide hint
Refer to integration techniques for polynomials.
Question 6.
Calculate the expected value (mean) of X when its PDF is given as f(x) = 6x(1-x) for 0 ≤ x ≤ 1.
Show hintHide hint
Distributing and integrating will be key here.

5 more questions in this section. Enroll free to practise them all.