13.1.3. Properties of PDF

Try these first

1. 1.

   What does non-negativity mean in the context of a PDF?

   Hint

   Think about the probabilities and their range.

2. 2.

   True or False: The total area under a PDF curve must equal one.

   Hint

   Consider probabilities summing to 100%.

3. 3.

   What is a key characteristic of a valid PDF?

   • It can take negative values
   • It must be non-negative
   • It can sum over to more than one

   Hint

   Remember, probabilities cannot be negative.

4. 4.

   True or False: The total area under a PDF equals zero.

   • True
   • False

   Hint

   Think about the definition of a PDF.

5. 5.

   Propose a PDF for a scenario in which the variable X represents time taken to complete a task and demonstrate how you would find the probability of completing the task within a specific timeframe.

   Hint

   Use the properties of uniform distributions.

6. 6.

   Create a continuous random variable with a given PDF and calculate the expected value and variance.

   Hint

   Work through the formula for expected value and variance iteratively.