6.7. Further Reading

Try these first

1. 1.

   Define a random variable.

   Hint

   Think about how outcomes of experiments can be quantified.

2. 2.

   Give an example of a discrete random variable.

   Hint

   Consider an experiment with a limited number of outcomes.

3. 3.

   What is a random variable?

   • A function relating outcomes to numbers
   • A fixed value
   • A type of probability distribution

   Hint

   Think about experiments and how outcomes can be represented.

4. 4.

   True or False: A PMF can sum to a number greater than one.

   Hint

   Consider the rules of probability.

5. 5.

   Given a discrete random variable representing the roll of two six-sided dice, calculate the PMF for the sum of the dice.

   Hint

   Think about all combinations that can lead to each sum.

6. 6.

   A continuous random variable X has a PDF of f(x) = 3x^2 for 0 ≤ x ≤ 1. Calculate the expected value E(X).

   Hint

   Integrate to find area and then multiply accordingly!