6.1. Random Variables: Definition

Try these first

1. 1.

   What is a random variable?

   Hint

   Think about how outcomes in experiments can be quantified.

2. 2.

   Give an example of a discrete random variable.

   Hint

   Consider things that can be counted.

3. 3.

   What are random variables used for?

   • To predict outcomes
   • To count items
   • To measure time

   Hint

   Think about where uncertainty is present.

4. 4.

   Is a temperature reading a discrete random variable?

   • True
   • False

   Hint

   Consider how temperature can change gradually.

5. 5.

   In a game, a player wins $0,$1, or $2 with probabilities 0.5, 0.3, and 0.2 respectively. Calculate the expected value of their winnings.

   Hint

   Use the expectation formula with given probabilities.

6. 6.

   A continuous random variable has a PDF given by f(x) = 3x² for 0 ≤ x ≤ 1. Find the expectation of this variable.

   Hint

   Integrate the product of x and the PDF within the defined limits.