6.2. Discrete Random Variables

Try these first

1. 1.

   What is a discrete random variable? Provide an example.

   Hint

   Think about outcomes of simple experiments.

2. 2.

   What does PMF stand for?

   Hint

   It's related to how we calculate probabilities for discrete variables.

3. 3.

   What does a discrete random variable represent?

   • Countable outcomes
   • Uncountable outcomes
   • Both countable and uncountable

   Hint

   Consider how many different outcomes can be listed.

4. 4.

   True or False: The PMF can take on negative probabilities.

   • True
   • False

   Hint

   Recall the basic properties of probability.

5. 5.

   A game involves rolling a fair cube three times. What is the probability of getting exactly two sixes?

   Hint

   Identify n, k, and p to use the binomial formula correctly.

6. 6.

   Given a random variable X with the following PMF: P(X=0) = 0.3, P(X=1) = 0.4, P(X=2) = 0.3. Calculate the variance.

   Hint

   You will need to find E[X²] first; sum the square of x times their respective probabilities.