13.1.2. What is a Probability Density Function (PDF)?

Try these first

1. 1.

   Define what a PDF is in your own words.

   Hint

   Think about how we visualize probabilities over intervals.

2. 2.

   What is the total probability in any PDF?

   Hint

   Recall the property of normalization.

3. 3.

   What does a PDF describe?

   • Discrete variables
   • Continuous variables
   • Both

   Hint

   Think about the characteristics of continuous versus discrete.

4. 4.

   The total area under the PDF curve for a continuous random variable is equal to:

   • 0
   • 1
   • Infinity

   Hint

   Remember the normalization property.

5. 5.

   Suppose a PDF is defined as f(x) = 3x^2 for 0 ≤ x ≤ 1. Calculate the probability that X falls between 0.2 and 0.5.

   Hint

   Remember to set up the integral properly and evaluate it.

6. 6.

   Given a normal distribution with mean 10 and variance 4, calculate the probability that a random variable X is less than 12.

   Hint

   Transform the problem to fit the standard normal distribution format.