Question

Suppose you have the following probability distribution.

State of nature Profit Level Probability
Optimistic $500 0.3
Most Likely 100 0.6
Pessimistic -400 0.1

What is the mean?

A. 68,100
B. 1.5
C. 261
D. 170
E. None of the above

Answer 1

To calculate the mean of the given probability distribution, we multiply each profit level by its probability and add them up, resulting in a mean profit of $170, corresponding to option D.

Step-by-step explanation:

The question asks for the mean of a probability distribution. To find the mean, also known as the expected value, we multiply each profit level by its corresponding probability and sum the results.

• For the optimistic state: $500 × 0.3 = $150
• For the most likely state: $100 × 0.6 = $60
• For the pessimistic state: -$400 × 0.1 = -$40

Now add these amounts: $150 + $60 - $40 = $170

Therefore, the mean profit is $170, which corresponds to option D.