7.2.8. Steps to Work with PDFs

Try these first

1. 1.

   What does PDF stand for?

   Hint

   It's essential in the probability.

2. 2.

   Name two common types of probability distributions.

   Hint

   Think of how probabilities can be evenly spread or clustered.

3. 3.

   What is the sum of all PDF values over its range?

   • Less than 1
   • Equal to 1
   • More than 1

   Hint

   Think about the entire probability space.

4. 4.

   A PDF can be negative.

   • True
   • False

   Hint

   Recall the foundational properties of PDFs.

5. 5.

   If a variable X has a uniform distribution between 0 and 16, what is the probability that X is less than 5?

   Hint

   Use the length of the interval method.

6. 6.

   A continuous random variable has a PDF given by f(x) = 3x^2 for 0 < x < 1. Find the mean of this distribution.

   Hint

   Use the definition of expected value with the PDF.