13.1.5. Common Probability Density Functions

Try these first

1. 1.

   What does a Probability Density Function (PDF) represent?

   Hint

   Think about how continuous variables behave.

2. 2.

   Is the probability at a single point for a continuous random variable zero?

   Hint

   Consider the infinite possibilities in a continuous range.

3. 3.

   What does the total area under the PDF curve equal?

   • 0
   • 1
   • 2

   Hint

   Consider the definition of probability.

4. 4.

   True or False: In a continuous distribution, the probability of a single point is greater than zero.

   • True
   • False

   Hint

   Think about the concept of continuous values.

5. 5.

   A continuous random variable has a PDF defined as f(x) = kx for 0 ≤ x ≤ 2, where k is a constant. Find k and then calculate P(0.5 ≤ X ≤ 1.5).

   Hint

   Remember to first find k by normalization.

6. 6.

   Given a Normal distribution with mean of 100 and standard deviation of 15, what is the probability of selecting a value between 85 and 115?

   Hint

   Calculate Z-scores from the provided values and refer to the Z-table.