Question

Determine whether the following can be probability distributions of a random variable which can take on only the values 1, 2, 3, and 4.

(a) f(1) = 0.19, f(2) = 0.27, f(3) = 0.27, f(4) = 0.18. (You can indicate whether it's a valid probability distribution or not.)

Answer 1

The function provided is not a valid probability distribution because the sum of the given probabilities is 0.91, which does not meet the requirement that the total sum of all probabilities must equal one.

Step-by-step explanation:

To determine whether the provided function represents a valid probability distribution for a discrete random variable, there are two main criteria that must be met:

1. Each probability must be between zero and one, inclusive.
2. The sum of all probabilities must equal one.

In the case of the given distribution: f(1) = 0.19, f(2) = 0.27, f(3) = 0.27, and f(4) = 0.18, we can do a quick check:

• All the given probabilities are between zero and one, meeting the first condition.
• We sum the probabilities: 0.19 + 0.27 + 0.27 + 0.18 = 0.91.

Since the sum of these probabilities is not equal to one, the given function does not meet the second condition, and therefore it cannot be a valid probability distribution.