12.9. Common Discrete Distributions and Their PMFs

Try these first

1. 1.

   Define a discrete random variable with an example.

   Hint

   Think of countable items.

2. 2.

   What does PMF stand for and what does it represent?

   Hint

   What does probability relate to in regards to outcomes?

3. 3.

   What is the PMF of a Bernoulli distribution?

   • p^x(1 - p)^{1 - x}
   • p(1 - p)^x
   • (n choose x)p^x(1 - p)^{n - x}

   Hint

   Remember the two outcomes of Bernoulli.

4. 4.

   True or False: The Poisson distribution can be used for modeling continuous random variables.

   • True
   • False

   Hint

   Consider the type of variable it models.

5. 5.

   Consider a biased coin, where the probability of heads is 0.7. If you toss it 10 times, calculate the probability of getting exactly 7 heads.

   Hint

   You'll need to calculate the binomial coefficient.

6. 6.

   A radio station receives an average of 5 calls per hour. What is the probability that it will receive exactly 3 calls in the next hour?

   Hint

   Apply the Poisson formula directly.