14.1.1. Random Variables

Try these first

1. 1.

   Define a discrete random variable.

   Hint

   Think of examples that can be counted, like the number of flaws in a batch of products.

2. 2.

   What is a continuous random variable?

   Hint

   Consider measurements like weight or time.

3. 3.

   What is the defining characteristic of a discrete random variable?

   • Can take any value
   • Is countable
   • Represents a probability density function

   Hint

   Remember examples with a limited number of outcomes.

4. 4.

   True or False: Continuous random variables only take exact values.

   • True
   • False

   Hint

   Think of real numbers in a range.

5. 5.

   Consider a game where you roll two dice. Define the joint distribution for the sums of the two dice.

   Hint

   Examine the possible pairs that lead to each sum.

6. 6.

   A manufacturer inspects a batch of products and records the number of defects and weight. How can you represent this using joint probability?

   Hint

   Consider how defects can relate to different weight categories.