Question

The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. Find the mean.

Answer 1

To find the mean of a probability distribution, multiply each observed value by its corresponding probability and sum the results.

Step-by-step explanation:

To find the mean of a probability distribution, we multiply each observed value by its corresponding probability and sum the results. In this case, we can calculate the mean by multiplying each number on the loaded die by its respective probability, and then adding up the products. Let's denote the numbers on the die as x and their respective probabilities as P(x). The formula to find the mean is:

Mean = Σ(x * P(x))

Using the values from the table, we can calculate the mean as follows:

Mean = (1 * 0.2) + (2 * 0.1) + (3 * 0.25) + (4 * 0.15) + (5 * 0.3)

= 0.2 + 0.2 + 0.75 + 0.6 + 1.5

= 3.25

Therefore, the mean of the probability distribution for the loaded die is 3.25.