7.3.. Non-negativity

Try these first

1. 1.

   What does non-negativity of a PDF mean?

   Hint

   Think about what probabilities represent.

2. 2.

   Can a PDF ever take negative values? Why or why not?

   Hint

   Recall the meaning of probability.

3. 3.

   What does the non-negativity property of PDFs imply?

   • PDF values can be negative
   • PDF values are always zero or positive
   • PDF values can exceed one

   Hint

   Remember how we categorize probabilities.

4. 4.

   True or False: A valid probability distribution can contain negative values.

   • True
   • False

   Hint

   Think about what a negative probability would represent.

5. 5.

   A researcher mistakenly models a random variable's PDF and allows negative values. Discuss the potential consequences this misinformation could lead to in statistical conclusions.

   Hint

   Consider the implications of statistical accuracy.

6. 6.

   Design a simple PDF for a random variable that can only take values in a range from 0 to 10, ensuring it respects the non-negativity condition. Outline your thought process.

   Hint

   Use straightforward mathematical functions for easy understanding.