EXAMPLE 4Recognizing valid discrete probability distributions

Identify which of the following is a valid discrete probability distribution.

  1. 1 10 100 1000
    0.2 0.4 0.3 0.2
  2. −10 0 10 20
    0.5 0.3 0.4 −0.2
  3. Red Green Blue Yellow
    0.1 0.3 0.4 0.2
  4. −5 0 5 10
    0.1 0.3 0.4 0.2

Solution

  1. This is not a valid probability distribution because the probabilities add up to 1.1, which is greater than 1.
  2. This is not a valid probability distribution because is negative.
  3. This is not a valid probability distribution for a discrete random variable because the values of are not quantitative.
  4. This is a valid probability distribution because the probabilities sum to 1, and each probability takes a value between 0 and 1.

NOW YOU CAN DO

Exercises 25–28.